Question

An electon in a box absorbs light. The longest wavelength in the absorbtion spectrum is 700 nm . How long is the box

Answer 1

Answer:

8.01 (10^-10) m

Explanation:

use the Particle in a box equation

E = (n^2) (h^2) / (8 m (L^2))

and energy of a particle as its wavelength equation

h c / lamda = E

combine the equations to get

h c / lamda =  (n^2) (h^2) / (8 m (L^2))

get L alone

L^2 = (2^2 - 1^2) h lamda / 8 m c

the longest wavelength is produced by a jump from the first excited state to the ground so

n = 2 to n = 1

so

L^2 = (n1^2 - n2^2) h lamda / (8 m c)

h = 6.6(10^-34) J*s

c = 3(10^8) m/s

m = 9(10^-31) kg

lamda = 700(10^-9) m

n1 =2

n2=1