Answers to Problems
Chapter 1
1. Time period is (1 + v/c)/(1 – β
2
)
1/2
5. 14%; 10 km
7. 0.9974c
9. (M
2
– m
2
) c
2
/2M; 224.6 MeV, 3.4 eV
11. 0.875c, 0.999994c
12. 287 km/s; 6556.7 Å
Chapter 2
1. 5800 K; for significant number of hydrogen atoms to be in the excited
states, kT ~ 10 eV
2. 7.13 × 10
3
J/s; 0.019 J/s
4. 19; 4 × 10
17
m
–2
s
–1
5. [2mc
2
(hv – ε) + h
2
v
2
– 2hv (2mc
2
(hv – ε))
1/2
cos φ] 2 Mc
2
5. θ = 180°; 2h
2 2
0
v /mc
2
7. 0.1484 Å, 0.1 Å; θ = 54°
8. [(m
2
c
4
+ h
2
v
2
)
1/2
– mc
2
]/hv; hv/2mc
2
; 10 keV
9. 1.2 Å; yes
10. n = 1, d = 0.5 Å
12. 0.7 MeV; 40 MeV
13. n ω
14. 0.5 × 10
–13
m; 25.3 MeV
16. 1/1836
17. 2
18.
/(2 )
2 2
;
1
2
s
s
s
mgs
n
g
n
−



ω
−






19.
(1 1)
2
e Bn
m
±
for parallel and anti-parallel cases
20. n ω
22. 1216 Å, 1026 Å
23. 6000 K
24. 14 K
Chapter 3
1.
1/2
1
s i n( / )
2
h
k a
a
k
 
 
π  
2. T = 4r/(1 + r
2
), r = (E + V 0 )
1/2
/E
1/2
, R = 1 – T
3. v = hn/4ml
2
= v/2l
4. A = (πa
3
)
–1/2
, a = 4πε 0 h
2
/me
2
, E = –
2
/2ma
2
; P = 13 e
–4
5. a = (km)
1/2
/2 . A =
1/2
5/4
1/4
(8/3) (2 )
a
π
S. H. Patil, Elements of Modern Physics,
https://doi.org/10.1007/978-3-030-70143-7
423
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Switzerland AG 2021