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

Answer:

Yes

Explanation:

$\nu_0=\frac {c}{\lambda_0}$

$\lambda_0$ is the threshold wavelength

$\nu_0$ is the threshold frequency = $5.6\times 10^{14}\Hz$

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

Applying the equation as:

$5.6\times 10^{14}=\frac {3\times 10^8}{\lambda_0}$

$\lambda_0=\frac{3\times 10^8}{5.6\times 10^{14}}\ m$

$\lambda_0=535.714\times 10^{-9}\ m$

$E_0=\frac {h\times c}{\lambda_0}$

Where,  

h is Plank's constant having value $6.626\times 10^{-34}\ Js$

So,

$E_0=\frac{6.626\times 10^{-34}\times 3\times 10^8}{535.714\times 10^{-9}}\ J$

$E_0=3.71056\times 10^{-19}\ J$

Given, $\lambda=475\ nm=475\times 10^{-9}\ m$

$E=\frac {h\times c}{\lambda}$

$E=\frac{6.626\times 10^{-34}\times 3\times 10^8}{475\times 10^{-9}}\ J$

$E=4.18484\times 10^{-19}\ J$

Since, E > E0, So it can eject.