Exam (elaborations)
Exam (elaborations) TEST BANK FOR Quantum Physics 3rd Edition By Steph
- Course
- Institution
Exam of 147 pages for the course TEST BANK FOR Quantum Physics 3rd Edition By Steph at UM (error)
[Show more]
Seller
Follow
COURSEHERO2
Content preview
, SOLUTIONS MANUALCHAPTER 1
1. The energy contained in a volume dV is
U(ν,T )dV = U (ν ,T )r 2 dr sinθ dθdϕ
when the geometry is that shown in the figure. The energy from this source that emerges
through a hole of area dA is
dAcos θ
dE(ν ,T ) = U (ν ,T )dV
4πr 2
The total energy emitted is
π /2 2π dA
dE (ν ,T ) = ∫ dr∫ dθ ∫ dϕU (ν,T )sin θ cosθ
cΔt
0 0 0 4π
dA π/2
= 2π cΔtU (ν ,T ) ∫ dθ sinθ cosθ
. 4π 0
1
= cΔtdAU (ν ,T )
4
By definition of the emissivity, this is equal to EΔtdA . Hence
c
E (ν, T ) = U (ν, T )
4
2. We have
c c 8π hc 1
w(λ ,T ) = U (ν ,T ) | dν / dλ |= U ( ) 2 = 5
λ λ λ e hc/λkT
−1
This density will be maximal when dw(λ ,T ) / dλ = 0 . What we need is
A /λ
d ⎛1 1 ⎞ 1 1 e A 1
= (−5 − (− )) =0
d λ ⎝ λ e − 1⎠
5 A / λ
λ λ e −1 λ e λ −1
6 5 A / λ 2 A /
Where A = hc / kT . The above implies that with x = A / λ , we must have
5 − x = 5e −x
A solution of this is x = 4.965 so that
, hc
λmaxT = = 2.898 × 10 −3 m
4.965k
In example 1.1 we were given an estimate of the sun’s surface temperature
as 6000 K. From this we get
28.98 × 10 −4 mK
λsun
max = = 4.83 × 10−7 m = 483nm
6 × 10 3 K
3. The relationship is
hν = K + W
where K is the electron kinetic energy and W is the work function. Here
hc(6.626 × 10−34 J .s)(3× 10 8 m / s)
hν = = = 5.68 × 10 −19 J = 3.55eV
λ 350 × 10 m −9
With K = 1.60 eV, we get W = 1.95 eV
4. We use
hc hc
− = K1 − K2
λ1 λ2
since W cancels. From ;this we get
1 λ1λ 2
h= (K − K 2 ) =
c λ 2 − λ1 1
(200 × 10 −9 m)(258 × 10−9 m)
= × (2.3 − 0.9)eV × (1.60 × 10 −19 )J / eV
(3 × 10 8 m / s)(58 × 10−9 m)
−34
= 6.64 × 10 J .s
5. The maximum energy loss for the photon occurs in a head-on collision, with the
photon scattered backwards. Let the incident photon energy be hν , and the backward-
scattered photon energy be hν' . Let the energy of the recoiling proton be E. Then its
recoil momentum is obtained from E = p 2c 2 + m 2c 4 . The energy conservation
equation reads
hν + mc 2 = hν ' + E
and the momentum conservation equation reads
hν hν '
=− +p
c c
, that is
hν = −hν '+ pc
We get E + pc − mc 2 = 2hν from which it follows that
p2 c 2 + m2 c 4 = (2hν − pc + mc 2 ) 2
so that
4 h 2ν 2 + 4 hνmc 2
pc =
4 hν + 2mc 2
The energy loss for the photon is the kinetic energy of the proton
K = E − mc 2 . Now hν = 100 MeV and mc 2 = 938 MeV, so that
pc = 182MeV
and
E − mc 2 = K = 17.6 MeV
6. Let hν be the incident photon energy, hν' the final photon energy and p the outgoing
electron momentum. Energy conservation reads
hν + mc = hν ' + p c + m c
2 2 2 2 4
We write the equation for momentum conservation, assuming that the initial photon
moves in the x –direction and the final photon in the y-direction. When multiplied by c it
read
i(hν ) = j(hν ') + (ipx c + jpy c)
Hence px c = hν ; pyc = − hν '. We use this to rewrite the energy conservation equation as
follows:
(hν + mc 2 − hν ')2 = m 2c 4 + c 2 ( px2 + py2 ) = m2 c 4 + (hν ) 2 + (hν ') 2
From this we get
⎛ mc 2 ⎞
hν'= hν ⎜ ⎟
⎝ hν + mc 2 ⎠
We may use this to calculate the kinetic energy of the electron
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller COURSEHERO2. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.28. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
81113 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now
Recently viewed by you
