Calculate the wavelength of the electromagnetic radiation required to excite an electron from the ground state to the level with n = 5 in a one-dimensional box 45.7 pm in length.

2.11 m

Explanation:

Given data

h=6.626×(plank constant)

L=45.7 pm

n=n2-n1

n=5-1

n=4

where,

n2=5

n1=1

To find:

E=?

λ=? (Wavelength)

solution

The energy stored in an electron at a specified level is given by;

E=×÷8m..........(1)

m=mass of electron(9.1×)

l=length of box

To find E

putting the value of given data in eq(1)

E=9.41×

To find λ

λ=hc/E............................(2)

c=3×(speed of light)

putting the value in eq 2 to find wavelength

λ=2.11 m

Note:

There is a chance in calculation error. but the method is correct to solve the problem.