Question

Would a photon with a wavelength of 475nm have enough energy to eject an electron from metal X? (frequency threshold= 5.6X10^14Hz) (Wavelength= 3.7X10^-19J)

Answer 1

Yes

Step-by-step explanation:

`\\u_0=\frac {c}{\lambda_0}`

`\lambda_0` is the threshold wavelength

`\\u_0` is the threshold frequency =
`5.6* 10^(14)\Hz`

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

Applying the equation as:

`5.6* 10^(14)=\frac {3* 10^8}{\lambda_0}`

`\lambda_0=(3* 10^8)/(5.6* 10^(14))\ m`

`\lambda_0=535.714* 10^(-9)\ m`

`E_0=\frac {h* c}{\lambda_0}`

Where,

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

So,

`E_0=(6.626* 10^(-34)* 3* 10^8)/(535.714* 10^(-9))\ J`

`E_0=3.71056* 10^(-19)\ J`

Given,
`\lambda=475\ nm=475* 10^(-9)\ m`

`E=\frac {h* c}{\lambda}`

`E=(6.626* 10^(-34)* 3* 10^8)/(475* 10^(-9))\ J`

`E=4.18484* 10^(-19)\ J`

Since, E > E0, So it can eject.