### Physics 4D HomeWork Even Problems Answers

Chapter 1

2)proof

4)t(ud)=0.4167 hr, t(c) = 0.4082 hr

10)a)8.33 x 10^-8 s b)24 m

12)a)70 beats/min b)31 beats/min

14)proof

24)0.982C

26)0.95C

30)a)2d/(c+v) b)(2d/c)SQRT((c-v)/(c+v))

34)a)83.5 m, 62.5m b)20.3m, 27.1m c)1.67hr d)1.47hr e)1.97hr f)#2 lives, #1 dies

36)a)0.943C b)2550m

Chapter 2

2)a)0.85c b)no change

6)proof

8)a)939.4 MeV b)3.01 x 10^3 MeV c)2.07 x 10^3 MeV

10)0.75c

28)a)4.00 x 10^-14 kg b)1.60 x 10^-12

Chapter 3

24)a)0.00243 nm b)74.4 eV

30)0.0120 nm

32)a)1.95 x 10^-3 eV b)0.0861 nm

46)22.9

48)a)1.01 x 10^-10 m b)81.1

Chapter 4

18) a)12.1 eV b)12.1 eV, 10.2 eV, 1.89 eV

24)a)102.517 nm b) p =6.47 x 10^-27 kg m/s, K=7.83x10^-8 eV

28)5.385 keV

36)a),b)worked out in lecture c) frequency of photon should approach frequency of rotation

for large quantum numbers.

42)1.89x10^6 m/s

44)a)oxygen b)41 nm, 33.8 nm, 30.4 nm

Chapter 5

2)a)0.0173 nm b)0.00536 nm

4)7.28 x 10^6 m/s

6)1.28 x 10^-4 nm

16) Vg = (3/2)Vp

18)3.51 x 10^-32 m

24)Did in class

30)a) 1.07 x 10^-17 kg m/s b) 6.2 x 10^-17 m

32)a)4.34 x 10^14 Hz b)691 nm c)3.30 x 10^-10 eV

Chapter 6

2)a)(4/L)^(1/2) b)0.409

6)Did in class

12)7.93x10^-10m

16) a)0.1955 b)0.3319 c)YES!!!

18)check graphically

24) a)alpha = mw/2h, E=(3/2)hf b)C = (32*alpha^3/Pi)^0.25

26)P(x)=1/(Pi*(A^2-x^2)^0.5)

28)a) did in class b)<x>=L/2, <x^2>=L^2/3

30)proof

32)<x>=0, <x^2>=h/(4Pimw), DeltaX = [h/(4Pimw)]^0.5

34)h/(4Pi)

Chapter 7

2)proof

4) 1.8x10^-4 mA

Chapter 8

4)a)results are similar to the 3D problem with the exception that you only have two component for the wavefunction.

6)Solve the TISE to find the wavefunction!!! The energy will be sharp. That is, you know the value of E exactly!!

10)a)3.65x10^-34 Js b)3.16x10^-34Js

12) a)& b) did in class c)graph d)proof e)0.496

18)a)6 b)-0.378 eV c)4.47 h/2Pi d)m = -4,-3,-2,-1,0,1,2,3,4; see example in class

22)5ao

24)=-27.2 eV, <k>=13.6 eV

26)0.176, 0.371

30)0.866h/2Pi

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