Question

For potassium metal, the work function φ (the minimum energy needed to eject an electron from the metal surface) is 3.68 × 10–19 J. Which is the longest wavelength of the following which could excite photoelectrons?

a. 550nm
b.500nm
c.450nm
d.400nm
e.350nm

Answer 1

A.
`\lambda_0=550\ nm`

Step-by-step explanation:

The work function of the potassium =
`3.68* 10^(-19)\ J`

For maximum wavelength, the light must have energy equal to the work function. So,

`\psi _0=\frac {h* c}{\lambda_0}`

Where,

h is Plank's constant having value
`6.626* 10^(-34)\ Js`

c is the speed of light having value
`3* 10^8\ m/s`

`\lambda_0` is the wavelength of the light being bombarded

`\psi _0=Work\ function`

Thus,

`3.68* 10^(-19)=\frac {6.626* 10^(-34)* 3* 10^8}{\lambda_0}`

`(3.68)/(10^(19))=(19.878)/(10^(26)\lambda_0)`

`3.68* \:10^(26)\lambda_0=1.9878* 10^(20)`

`\lambda_0=5.50* 10^(-7)\ m`

Also,

1 m = 10⁻⁹ nm

So,

`\lambda_0=550\ nm`