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 of 40.0 pm in legth
The wavelength of electromagnetic radiation required to excite an electron from the ground state to the level with n=5 in a one-dimensional box can be calculated using the formula:
λ = 2L/n
where:
λ = wavelength
L = length of the one-dimensional box (40.0 pm = 40.0 x 10^-12 m)
n = quantum number of the excited state (n=5 in this case)
Plugging in the values:
λ = 2(40.0 x 10^-12 m)/5
λ = 80.0 x 10^-12 m / 5
λ = 16.0 x 10^-12 m
λ = 16.0 pm
Therefore, 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 of 40.0 pm in length is 16.0 pm.