Friday, September 3, 2021

Solutions To Physics Problems (Set 3)

 1) The de Broglie wavelength is given by:  l D = h/p


where h is the Planck constant and p is the momentum. (In this case, we need to use the version h = 4.13 x 10-15 eV*s)

Since the problem information provides an energy E = 1 MeV, then we need p in the form:

p = [2mE]1/2

These units mean it will also be easier to do the problem by using atomic mass units in MeV. Thus, 1 u = 931 MeV/c2, so for an alpha particle (m =He4) we need 4u = 4 (931 MeV/c2)

Then:

l D = (4.13 x 10-`5 eV*s)/ 2[4 (931 MeV/c2)] = 10-14 m

l D = 10-12 cm


2) For a Young double slit, d sin (q) = m l

gives the bright fringe, where m is the order and l the wavelength. Since the distance to the screen is much greater than the height of the bright fringe, sin (q) = x / D, where x is the height and D is the distance to the screen. So:

D (x) d/ D = l



D(x) = Dl/ d

then: D(x) = (3 x 103 mm) (6 x 10-5 cm/ 0. 2 cm) = 0.9 mm

3) This application makes use of the
 energy-time uncertainty principle:

D(E) D(t) = h/ 2 π

Here, t = the mean lifetime of the excited state = T(½) = 8 x 10-8 sec

And E=
 the half-width of the excited state = E(½)

then:

E(½) T(½) =h/ 2 π = 1.03 x 10-34 J-s

E(½) = (1.03 x 10-34 J-s)/ (8 x 10-8 sec) = 1.2 x 10-27 J

But: 1.6 x 10-19 J = 1 eV (electron -volt)

so: E(½) = 10-9 eV



4) We have: N = No  exp (-lt)


let t = T1/2  the half life, then:

N = No  exp (-lT1/2)

or N / No   = ½ =  exp (-lT1/2)


and: - ln 2 = (-lT1/2)



 T1/2   = (ln 2)/ l


5) The "mean life" of one of the atoms in the sample will be:

= ∫ (from 0 to oo) exp (-lt) dt

= 1/ l {exp (-lt)] 0 to oo

= 1/l [exp (-l*0)] = 1/l [exp(o)] = 1/l

since exp(0) = 1

6) We need to apply both conservation of energy, and conservation of momentum. (There are two distinct angles involved, φ  and q)

For the conservation of energy: T1 = T1' + T2'

for the conservation of momentum : P1 = P1'cos(q) + P2' cos (φ)

and: 0 = P1'sin(q) - P2' cos(φ)

p = [2mT]1/2 (see also #31)



A head-on collision implies the unique values:  φ = 0 and q = 180 deg

so:

[2m1T1]1/2 = ([2m1T1']1/2 ) cos(180) + ([2m2T2']1/2 ) cos (0)

But cos (0)= 1 and cos (180) = -1, so:

[2m1T1]1/2 = - [2m1T1']1/2 + [2m2T2']1/2

Now, since T1 = T1' + T2':

2m1T1 + 4m1 [T1T1']1/2 = 2m2T2' - 2m1T1'

4m1 [T1T1']1/2 = - 2m1T1' + 2m2T2' - 2m1(T1 - T2')

whence:

2m1[T1(T1 - T2')]1/2 = (m1 + m2)T2' - 2m1 T1

4m12 T1 (T1 - T2') = (m1 + m2)2T2' + 4m12T12 - 4m1T1(m1 + m2)T2'

(m1 + m2)2 T2'2 - 4 m1m2T1T2' = 0

Then:

T2/T1 = 4 m1m2/ (m1 + m2)2


7) We sketch the HCl molecule, so:

H o<-------- ---------x--------->O (Cl)

And 1.27 Å defines the entire distance as shown (arrow to arrow) and let 'x' be the distance from the center of mass (cm) to the H atom. (Recall 1Å = 10-8 cm).

Then:

x = 36(1.27Å - x)

37x = 36 (1.27 Å)

x = 36(1.27 x 10-8 cm)/ 37

m(p) = 1.67 x 10-24 g (mass of proton)



The moment of inertia I is given by:

I = m(p)2 x2 + 36 m(p) [(1.27 x 10-8 cm) - x]2

I = (1.67 x 10-24 g)(36/37)2 + 36/(37)2 [(1.27 x 10-8 cm)]2

I = 2.6 x 10-40 g-cm2


8) The Lande g-factor is defined:

g = [ J(J+ 1) + S(S +1) - L(L +1)/ 2J(J + 1) ] + 1

From our previous exposure to quantum mechanics

See, e.g.

http://brane-space.blogspot.com/2010/07/l-s-coupling-problem-solutions-and-more.html

and:

http://brane-space.blogspot.com/2010/07/more-quantum-problems.html

the 1D 3/2 state implies: L = 2, S = 1 and J = L + S = 2 + 1 = 3

then:

g = [3(3 + 1) + 1(1 + 1) - 2( 2+ 1)/ 2(3)(3 + 1)] + 1 = 1.33


9) Recall the nuclear relation:

f = M(A, Z) - A'/ A

and that graphing this vs. A yields a constituent mass 1.0085A. Thus the total binding energy is: (0.0085A) x (931 MeV) or about 7.9 MeV per nucleon.

10) Here, it's important to recognize 2144 cm-1 as the wave number, k. Also:

k = f/c = 2144 cm-1

then the frequency:

f = kc = (2144 cm-1) (3 x 1010 cm/sec) = 6.43 x 1013/s


11) Since the current decreases uniformly, we don't need di/dt and can instead make use of the finite difference:  D(I)/  D(t)

And  we know the voltage:


V = L [ D(I)/  D(t) ] = 0.25 H[ 2A/ (1/16s)]

Therefore:  V = 8 volts


42) Earth's atmosphere extends about 50 miles. If we assume the density of air to be constant:

p2 - p1 = r g(z2 - z1)

where p2, p1 are the different pressures at heights z2 and z1, respectively, and r is the air density with g the acceleration of gravity.

We can form a simple proportion based on the simplifying assumption:

(p2 - p1)/ p2 = (z2 - z1)/z2

p2 is what we need to find, and z2 is the height for 50 miles or ~ 50 x 5,000' = 250,000'.

whence:

(z2 - z1) = 200'

(p2 - p1)/ p2 = (z2 - z1)/z2 = 200'/ 250,000' = 0.0008

so:

(p2 - p1) = 0.0008 (p2)

p1 = p2 - 0.0008 (p2) = p2 =  76 Hg


13) For this solution, we let all quantities inside the sphere be denoted by (1) and all the quantities outside by (2).

By Gauss' law:

4 π r2 E1 = 4 π r(4 πr2/ 3)

where r (charge density) = 3 q / (4 π a2)

Therefore, E1 = qr/ a3

Further the associated energy is obtained via integration:

W1 = 1/ 8 π [∫ (0 to a) E12 (dA)

= 1/ 8 π [∫ (0 to a) (qr/ a3)2 (4 π r2) dr

W1= q2/ 10a

By Gauss' law:

4 π r2 E = 4 πq

E2 = q/ r2

W2 = 1/ 8 π [∫ (a to oo) (q/ r2)2 (4 π r2) dr

W2 = q2/2 [∫ (a to oo) dr/ r2]

W2 = q2/ 2a

Therefore: the total electrostatic energy W = W1 + W2

W = q2/ 10a + q2/ 2a = 3q2/ 5a


14) It helps here to sketch the circuit ( see graphic) and make use of angular frequency, w


From this, the total impedance is (bear in mind j = [-1]-1/2:

ZT = 1/ j wL + 1/ (1/ jw C1) + 1/ (1/ jwC2)

ZT = 1/ jwL + jw( C1 + C2)

ZT = j[ - 1/wL + w(C1 + C2)]

ZT = -1/wL + w(C1 + C2) = 0 at the natural frequency

so:

w2 = 1/ L(C1 + C2)

w = [1/ (10-5) (30 x 10-6)]1/2

w = 105 [1/3]1/2

w = 57,735 /s = 2 π f

so the natural frequency f  =  w/ 2 π   = 9, 189 /s

or about 9.2 kilocycles per second


15) From thermodynamic relations we have:

C V dT = C p - C v / (V/ T) V dV

Then:

(T/V)s= (C p / C v - 1) (T/V) p

But:

(¶T/ V) p = T/V since T = PV/ nR

dT/ T + (C p/ C v - 1) (dV/V) = 0

Integrating both sides:

TV^ (C p/ C v  - 1) = k

PV^ (C p / C v ) /  nR = k

PV^(C p/ C v ) = k/ nR

Then:

n = k/ PV^[C p/ C v ] R

Media Still Can't Comprehend That Social Security Cannot Become "Insolvent"

 Reading an AP report in The Denver Post 3 days ago, we learn that on account of Covid 19: 

"The new projections in the annual Social Security and Medicare trustees reports indicate that Social Security’s massive trust fund will be unable to pay full benefits in 2034 instead of last year’s estimated exhaustion date of 2035. For the first time in 39 years, the cost of delivering benefits will exceed the program’s total income from payroll tax collections and interest during this year. From here on, Social Security will be tapping its savings to pay full benefits."

Which begs the question of why the headline read: 'COVID Recession Pushed Social Security Insolvency Up By A Year.'

But this is wrong, given Social Security has no creditors, hence cannot become "insolvent" - meaning owing an existing debt to a company or bank or other financial entity.   The inability to pay a fraction or all of projected benefits is not the same as a private "debt" where actual insolvency would enter if left unpaid. 

The truth is that a holder of private debt, like a household, has a very different relationship to debt than the U.S. government which issues its own currency. For families and businesses, paying back debt means they either have to sacrifice current consumption or become insolvent and file for bankruptcy.  But the government doesn’t have this same constraint. You’ll rarely hear this stated, but the government’s ability to spend now is actually independent of how much debt it holds and what it spent yesterday.

To put it another way: Technically one can remove the $2.9 trillion the government owes the Social security Trust Fund (because of repeated raids or "borrowings") from the total National Deficit because Social Security has no EXTERNAL "collectors". It is in fact the government that OWES Social security not the other way around. Thus, the alleged $22 trillion deficit is actually more like $19 trillion.


Paul Krugman made an analogous point in a NY Times piece some months ago, i.e.that while family finances are limited by the family income, and hence a family cannot spend more than it earns,  the federal gov't can print as much money as it needs to. Yep, debt is generated but in its own currency.  Also the debtor here is also the creditor so there's no problem. But the family has to answer to outside banks, credit card issuers, collectors etc.  So the family debtors are not the same as the creditors.   Nor can the family just print money to pay off its outside obligations, whether an auto loan, mortgage or medical bill.


Some nervous Nellies prattle about government ever paying back a huge debt owed to beneficiaries - say to make the Social Security system liquid again (without printing $$).. This is straightforward: simply raise taxes, and specifically do away with the Payroll Tax cap. (Also referred to as the "taxable maximum" or the Social Security tax cap.)  With the cap gone, every manjack will have to contribute to S.S. via payroll taxes,  especially the wealthier citizens now escaping it (and who often draw on it in their elder years.)


Of course, the enemies of Social Security - and there are many - continually go back to the same old tool box to make attacks, hoping that some of it will stick.  Alas, a lot of it has, including that the Trust Fund is full of useless IOUs. But this is why smart people need to do themselves a favor and inform themselves on the facts. No better book can be found right now than 'Social Security Works' by Nancy J. Altman and Eric R. Kingson, which in their Chapters 8, 10 totally demolishes this "IOU" nonsense, showing these bonds carry the same weight as those dispensed to other countries, including China. In other words, they carry "the full faith and credit of the U.S. government" and - if ever betrayed - will show this nation can't be trusted to pay its just debts.


As to the staying power and importance of Social Security, we read (p. 23):


"Social Security transformed the nation. It eradicated what was once a primary anxiety for the majority of Americans: the terror of growing old penniless, dependent and vulnerable. It provided basic economic protection previously not available to most households."


This basic economic security is exactly what drives Social Security's opponents nuts. They hate to see anyone collecting a check just for breathing. At the very least, they insist, the money ought to be "privatized" - put into special investment accounts (with the costs of administration vastly greater than the 1 penny per dollar rate for S.S.) and subject to the vagaries of the stock market.


That basic security is undermined each time a sloppy media portrays the program inaccurately or repeats codswallop like the program will become "insolvent."


See Also:

by Joan McCarter | September 7, 2021 - 7:36am | permalink

— from Daily Kos

Well how about this.

Rep. John Yarmuth isn’t just any old congressperson. He’s chair of the House Budget Committee, and having this basic truth said out loud—“We can spend whatever we need to spend in the interest of serving the American people”—is progress. It’s especially key for a budget leader right now as Congress is putting together the budget reconciliation bill for President Joe Biden’s Build Back Better, the plan that could truly be transformative for America. It’s essential that the deficit peacocks are answered—like Sens. Kyrsten Sinema and Joe Manchin, who continue to insist that the number is too big even though they won’t say what needs to be sacrificed.

Thursday, September 2, 2021

Texas Version Of Taliban Imposes Draconian Abortion Law - Time To Boycott & Strike

 The Taliban has now resurfaced in Texas, thanks to a fascist Supreme Court that has allowed an illegitimate Texas abortion law to pass, overturning 50 years of precedent.  As of September 1, this misbegotten law bans abortions after six weeks, before most women even know they are pregnant. The Supreme Court has ultimately allowed Roe v. Wade to fall in the state of Texas. There'd be no difference - let us note - if the Taliban had actually taken over Texas. 

As Janice put it, what we are seeing is the rise of a theocracy in Texas, that even the odious Taliban would be proud of.  And behold the Supreme Court have become the accomplices of this Texas Taliban by not blocking a "law" that clearly violates the Constitution.


It gets worse:  This law is designed to permit any individual or organization in the country to sue Texans who help people access abortion care. States are usually responsible for enforcing anti-abortion laws, but S.B. 8 was written to rely on individuals to enforce the law in an attempt to shield it from the federal courts and questions of its constitutionality.

S.B. 8 puts a $10,000 bounty on anyone that helps someone obtain an abortion in Texas, including doctors who provide care, counselors and clergy members, family, friends or even rideshare drivers.  Thus, anyone can be "deputized"  as an instant enforcer or vigilante.  Thus,  given the law is supposed to be enforced by everyday citizens, there’s no single Texas official whom abortion rights advocates can sue to block the law, as they typically would in such cases.

We are already hearing that clinics in Texas have canceled appointments, leaving people with few options but to travel outside of the state to receive care -- if they can even do that.   Again, little difference - other than possible beheading of abortion providers- had the actual Taliban moved into the Lone Star state and took over.   

The thing that most enrages Janice - and I share that outrage - is there are no exceptions for rape or incest.  Exactly the same outcome you'd expect under a Taliban governance. The clear response for now - an immediate and powerful one- would be to follow Elie Mystal's advice on ALL In last night:  Joe Biden issues an executive order for federal marshals to accompany any woman desiring an abortion in TX to go a clinic.  Federal troops could also be called in to protect providers.   The basis?  Invoke "qualified immunity" - so often used to protect cops and CIA agents.  In this case, use it to make Texas abortion providers federal officials who will have qualified immunity—operating under the federal government's authority and protection.

Another solution, somewhat similar, has been offered by Jennifer Rubin:


My own suggestion is less dramatic: organize and call for major boycotts of all state products, and then go on an all -out strike - every critical worker in every Texas city, town.   Texan authorities have to be brought to their knees pronto and this is the only way I see to do it. And yeah, there may be some collateral damage.  But the worse offense is allowing a fascist violation of the Constitution to stand.

A more long term solution is to pack the Supreme Court with at least three more liberal justices, e.g.

As for the women of Texas, many of them will get abortions despite the new law, either by crossing borders or by purchasing abortion pills on the internet. This is a certainty.

Meanwhile, the 'pro-life' hypocrites of the anti-abortion side will continue to ignore those already born - their nutrition, health and welfare-  in favor of the rights of unborn protoplasm.

See Also:
And:
And:
And:

GOP Thug Tactics - And Why Trump Traitors Should Not Be Treated Like BLM Protesters

 

                     Trumper traitors want to be treated like BLM protesters.
                           Then why aren't they being given up to 5 years in prison?

The sheer gall of the Repuke pro-Trump traitors - including House members like Kevin McCarthy and Jim Jordan - is mind boggling.   Here we had McCarthy, day before yesterday, having the nerve to issue Mafia -like threats against telecom companies if they complied with House Select Committee subpoenas to turn in phone records of 11 GOP traitors.  (The committee  asked 35 companies to retain phone records and other information related to the attack  before the return of congress after its recess.)

This mega-Turd Traitor  speciously warned any such compliance would be against "federal law" and "subject to losing their ability to operate in the United States."  Adding:

"A Republican majority will not forget and will stand with Americans to hold them fully accountable"

Transl. A  Reepo "majority"  will stand with other American traitors and Trump lapdogs to try to impose their fascist will upon companies obeying a lawful subpoena. 

Of course this is all bluff and bollocks given: a) There is no guarantee there will be any future Reepo majority given these traitor scum will have to face hours of  Dem ads before the midterms showing their violent insurrection, and b)  it is actually McCarthy's threats - as Rep. Eric Swallwell noted (yesterday on 'Deadline White House') - that rise to the level of federal crime and obstruction of justice for a lawful investigation. 

This is also why today's WSJ editorial ('The Democratic Norm Breakers') is full of crap.  Claiming:

Critics feared that Speaker Nancy Pelosi’s probe of the Jan. 6 Capitol riot would be partisan, and the latest proof are subpoenas for the private phone records of House Republicans. This is a violation of political norms that Democrats will come to regret.

 Oh, please, get over your fulsome selves!  Those are material records pointing to likely conspiracy between the grand Traitor Trump and his degenerate allies in congress. 

But why be surprised?  Of course the WSJ has been soft soaping and minimizing the insurrection since Day 1 - with the exception of the occasional column from Peggy Noonan.

These editors also know - like the rest of us - that  McCarthy is crapping his pants because he knows (and they know) he's involved in sedition up to his eyeballs.  We know he spoke with Traitor-in-chief Trump on the day of the Capitol attack and also can be called as a potential witness in the probe.  He knows that too, hence the 'Goodfellas' posturing.

What was especially choice is this ragged ass rat bloviating about "standing with Americans." 

But McCarthy and his fascist thugs don't  "stand with me" or with any of the 81 million Americans who support our actual laws and the Constitution.  

The ones who need to be held fully accountable  are those on the pro-Trump,  pro -sedition,  pro-insurrection side.  

But this is only one sorry aspect of the 'pukes continued efforts to sweep their crimes under the proverbial rug.   Or to whitewash the treachery of January 6th into a simple case of "political protest".  No it wasn't it was treason, pure and simple.

But given this  concerted GOP whitewashing effort, it's a common refrain from some of those charged in the Jan. 6 insurrection and their Republican allies to claim unequal treatment.  I.e.  The Justice Department is treating them harshly "because of their political views" while those arrested during last year’s protests over racial injustice were given leniency.

Horse manure given the court records tell a different story.

An Associated Press review of court documents in more than 300 federal cases stemming from the protests sparked by George Floyd’s death last year shows that dozens of people charged have been convicted of serious crimes and sent to prison.  In other words, the BLM protesters drew much more severe punishment and mainly for property crimes.

The AP found that more than 120 defendants across the United States have pleaded guilty or were convicted at trial of federal crimes including rioting, arson and conspiracy. More than 70 defendants who’ve been sentenced so far have gotten an average of about 27 months behind bars. At least 10 received prison terms of five years or more. NONE of the Trump scum traitors have received anything like that.

The dissonance between the rhetoric of Capitol insurrectionists and their supporters and the record established by courts highlights both the racial tension inherent in their arguments — the pro-Donald Trump rioters were largely white and last summer’s protesters were mostly Black — and the flawed logic  at the heart of their claims.  To wit that protesters trashing a CVS pharmacy is worse than trashing the seat of our government and attempting to overturn an election. As Ali Velshi explained on his Jan. 17  MSNBC show:

"For starters, the Capitol is not a liquor store. When a mob breaks the Capitol buildings windows it is not criminal mischief but an assault on democracy itself and decency. That's the point, violence must always be understood in context."

Indeed,  as I wrote in the immediate wake of the Jan. 6 domestic terror event:

"If it was a mob of Muslim terrorists they'd all have been shot dead, but not these white domestic terrorists - who held the Capitol hostage for hours, carrying their Confederate traitor flags, invading the Senate chamber, and the House."

Yet these traitors are being rehabilitated in memory as I write.  Ashli Babbit is now elevated to a martyr, despite being among the first to try to break into the chamber  - only  stopped by Capitol cop Michael Byrd's bullet (after he warned her).   Then the remaining  rabble are being depicted as  "political prisoners" as opposed to traitors who merit hanging.

In the words of Kent Greenfield, a professor at Boston College Law School in respect to the BLM protesters:

“The property damage or accusations of arson and looting from last year, those were serious and they were dealt with seriously.  But they weren’t an attack on the very core constitutional processes that we rely on in a democracy, nor were they an attack on the United States Congress,”   

Janice herself pointed out if all those attacking the Capitol were black they'd have all been shot dead and there'd have been literal tons of heavy artillery in the streets.  In the actual case of these white terrorists let us note that had the National Guard not arrived in time,  many lawmakers might have been killed.    See e.g.

Trumpists intended to take members of Congress hostage, hold show trials, conduct executions  


 At least 11  GOP  House members are suspected to have colluded with Trump in preparing for the insurrection on January 6th.  But phone records and other materials are needed to corroborate it, hence the Select Committee's telling telecoms not to destroy phone records.  This is exactly why the maggot McCarthy is so petrified and why he's resorted to authoritarian thug- speak to try to intimidate telecom companies.   It is also why the Wall Street Journal editors insist in talking shit like (ibid.):

Republicans are furious, and rightly so. Indiana Rep. Jim Banks noted in a letter to Mr. Thompson that this “authoritarian undertaking” would depart “from more than 230 years of Congressional oversight.” 

No, imps, they are 'rightly furious' because they damned well know they will be exposed as the traitors  they are - working in league with Trump!  The "authoritarian undertaking"  balderdash is also choice in trying to turn the tables on the proven Trump authoritarianism to project it onto the Dems.   But most intelligent Americans will see through this blather, despite efforts to misdirect and obfuscate, e.g..   

Our legal sources say the subpoenas may violate the Constitution’s Speech and Debate Clause because Congress can’t pass a law that would limit Members’ speech

Better fire your legal sources and hire better ones, asswits. Because there is NO speech protection for those who help to incite insurrection, or engage in sedition!

Meanwhile, the inquiring mind must ask why the WSJ is so hard bent to protect traitors, like Kevin McCarthy with his Mafia threats. 

The despicable cretin Marjorie Taylor Green is no better, recently warning on FOX about shutting down the telecoms if they surrender phone records to the Select Committee. This on the heels of her FOX appearance stating those who advise others to get vaccines ought to be shot. Yet another reason this scurrilous traitor ought to have been hung by now with the others - especially the Johnny Reb turncoat Cawthorn.

Cawthorn spouted extremist and incendiary rhetoric about the Jan. 6 defendants and GOP claims about stolen elections.  This disreputable piece of dog dung actually called the Jan. 6 traitors -  who have been charged with crimes related to the Capitol insurrection -  "political hostages."   Further, proving he merits the gallows, he suggested breaking these vermin out!  In the words of this cockroach:

"The big problem is, we don't actually know where all the political prisoners are, and so if we were to actually be able to go and try and bust them out,"

The smarmy southern punk actually bemoaned not knowing the location of the jailed traitor rats, which prevented him and his ilk liberating them from federal custody.

Why isn't this POS behind bars?  Why isn't Matt Gaetz, Marjorie Taylor Greene and Kevin McCarthy?  Are we just going to allow them to descend to thug tactics and threats against the nation and Constitution?  


Enough is enough.  Now all the renegade traitors like Madison Cawthorn, Jim Jordan, Matt Gaetz, Kevin McCarthy and Marjorie Taylor Greene need to pay a price.  Being hung, drawn and quartered for starters.  But for now we'll settle for expulsion from the House for sedition.

See Also:

by Cody Fenwick | August 31, 2021 - 7:53am | permalink


Wednesday, September 1, 2021

More Physics Problems From Past GRE Papers (3)

TIME:  30  Minutes 

 1) Find the de Broglie wavelength associated with an alpha particle emitted with a kinetic energy of 1 MeV by the nucleus of an atom of radon.

2) Two slits are placed 2 mm apart and 300 cm from a screen. When light of 6000 A (angstroms) is used find the separation between the bright lines of the interference pattern in mm.

3) If the mean lifetime of the excited state of Cd 111 is T1/2
= 8 x 10 - 8 sec, find the half-width of the excited state.

Questions 4 and 5:

 The decay of a radioactive sample obeys the following relation:

N = No  exp (-lt)

where N is the amount of the sample at some time t, and No is the amount of the sample at an initial time to = 0.

4) Find the half -life of one of the atoms in the radioactive sample.

5) Find the mean life of one of the atoms in the radioactive sample.

6) By what fraction is the kinetic energy of a neutron (mass m1) decreased in a head-on elastic collision with an atomic nucleus (mass m2) initially at rest?

7) If an HCl molecule has an inter-nuclear distance of 1.27 A and the atomic weight of a Cl atom is 36, find the moment of inertia of the molecule about the center of mass.

8) Find the Lande g-factor for an atom in the state 1D 3/2.

9) Estimate the average binding energy of a nucleon in the nucleus of an atom.

10) In the near infrared spectrum of carbon monoxide, there is an intense band at 2144 cm-1. Estimate from this the fundamental vibration frequency of CO.

11) Find the voltage induced in a coil with an inductance of 0.25 H (henries) when the current is decreased uniformly from 2 amperes to zero amperes in 1/16 sec.

12) Assuming the density of air to be constant near the Earth's surface, and the barometric pressure at sea level is 76 Hg, estimate the barometric pressure at an elevation of 200' above sea level.

13) A sphere of radius a has uniform charge density of q distributed within it. Find the total electrostatic energy of this system.

14) An oscillating circuit contains an inductance of 10 m h (micro-henries), a capacitor of 5 mf (micro-farad) and a capacitor of 25 mf, all in parallel. Find the natural frequency, f, of this circuit.

15) The relation between pressure and volume in an adiabatic expansion is:

pvn = k.

If the specific heat at constant pressure is c p and the specific heat at constant volume is c v, then n = ?