Answers to In-Class Problems #4

1.) speed = 343.5 m/s at 20ºC

u = 261.6 s^-1

l = ?

speed = lu

343.5 m/s = l(261.6 s^-1)

l = 1.313 m

time to go 30.0 m = ?

speed = d/t

343.5 m/s = (30.0 m)/t

t = 0.0873 s

2.) Cs:

F = 3.43 x 10^-19 J

u_o = ?

F = hu_o

3.43 x 10^-19 J = (6.626 x 10^-34 Js) u_o

u_o = 5.18 x 10¹⁴ s^-1

c = lu

2.998 x 10⁸ m/s = l(5.18 x 10¹⁴ s^-1)

l = 5.79 x 10^-7 m (579 nm or yellow light)

Se:

F = 9.5 x 10^-19 J

u_o = ?

F = hu_o

9.5 x 10^-19 J = (6.626 x 10^-34 Js) u_o

u_o = 1.43 x 10¹⁵ s^-1

c = lu

2.998 x 10⁸ m/s = l(1.43 x 10¹⁵ s^-1)

l = 2.1 x 10^-7 m (210 nm or uv light)

3.) l = 520 nm = 5.2 x 10^-7 m

watts = 10 J/s

a.) E = hu

u = c/l

E = (hc)/l

E = [(6.626 x 10^-34 Js)(2.998 x 10⁸ m/s)]/(5.2 x 10^-7 m)

E = 3.8 x 10^-19 J

b.) 10 J/s, how many photons in 1 s?

(10 J)(1/3.8 x 10^-19 photons) = 2.6 x 10¹⁹ photons

4.)a.) E_k = 1.20 x 10⁷ J/mol

m_e = 9.11 x 10^-31 kg

l = ?

l = h/p = h/mv

E_k = (1/2)mv²

1.2 x 10⁷ J/mol = (1/2)(9.11 x 10^-31 kg)(6.022 x 10²³)v²

v = 6.614 x 10⁶ m/s

l = (6.626 x 10^-34 Js)/[(9.11 x 10^-31 kg)(6.614 x 10⁶ m/s)

l = 1.10 x 10^-10 m

b.) v = 353 m/s

m = (4.0026 g/mol)[(1/6.022 x 10²³)][(1 kg/1000 g)] = 6.6466 x 10^-27 kg

l = h/mv = (6.626 x 10^-34 Js)/[(6.6466 x 10^-27 kg)(353 m/s)]

l = 2.82 x 10^-10 m

c.) v = 299 m/s

m = (83.80 g/mol)[(1/6.022 x 10²³)][(1 kg/1000 g)] = 1.392 x 10^-25 kg

l = h/mv = (6.626 x 10^-34 Js)/[(1.392 x 10^-25 kg)(299 m/s)]

l = 1.59 x 10^-11 m

d.) v = 65 km/hr

m = 140 g = 0.140 kg

v = (65 km/hr)(1000 m/km)(1 hr/3600 s) = 18.1 m/s

l = h/mv = (6.626 x 10^-34 Js)/[(0.140 kg)(18.1 m/s)]

l = 2.6 x 10^-34 m