Quantum Mechanics

DAMON

2015-04-13 7:55 pm

1. (a) Find the excitation energy from the ground level to the third excited level
for an electron confined to a box that has a width of 0.120 nm.

(b) The electron makes a transition from the n = 1 to n = 4 level by absorbing
a photon. Calculate the wavelength of this photon.

回答 (1)

天同

2015-04-14 3:58 am

✔ 最佳答案

(a) Use equation En = (n.h)^2/8mL^2
where En is the energy of electron at n-th quantum state
h is Planck's constant (= 6.63 x 10^-34 m^2.kg/s)
m is the mass of electron (= 9.1 x 10^-31 kg)
L is the length of the box (= 0.12 x 10^-9 m)

Hence, E3 = (3 x 6.63x10^-34)^2/[8 x 9.1 x 10^-31 x (0.12x10^-9)^2] J

(b) E4 - E1 = (h^2/8mL^2).(4^2 - 1^2) J = 15h^2/(8mL^2)
Since energy of photon = hc/入
where c is the speed of light (= 3 x10^8 m/s) and 入 is the wavelegth in metre

Thus, 15h^2/(8mL^2) = hc/入
入 = 8mcL^2/15h

substitute the values of m, c , l and h to evaluate 入.

Please refer to the web-page for derivation of the formula:
En = (n.h)^2/8mL^2

http://bouman.chem.georgetown.edu/S02/lect13/lect13.htm

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