Question

What is the energy of blue light with a wavelength of $545nm$?

Answer 1

Hint : The photoelectric effect occurs as light shines on a metal surface and causes electrons to be ejected from the metal. A photon is an electric wave-particle of zero mass and a quantum of energy. The $E = hv$ equation is used to quantify the energy in photons of light.

Complete Step By Step Answer:
To calculate the energy, the formula used is $E = hv$.
Where, $h$ is the plank’s constant whose value is $6.626 \times {10^{ - 34}}joule.{\sec ^{ - 1}}$
and $v$ is the frequency.
First, we need to calculate the value of $v$ as it’s not mentioned in the question.
We know that, $c = \lambda v$
Where,
$c$is the speed of light
$\lambda $is the wavelength and
$v$is the frequency.
It’s given in the question that $\lambda = 545nm = 545 \times {10^9}m = 5.45 \times {10^7}m$
Substituting the values we get,
$
  3 \times {10^8} = 5.45 \times {10^{ - 7}} \times v \\
  v = \dfrac{{3 \times {{10}^8}}}{{5.45 \times {{10}^{ - 7}}}} \\
  v = 5.50 \times {10^{14}}{\sec ^{ - 1}} \\
 $

Now, substituting these values to the main equation we get,
$
  E = hv \\
  E = 6.626 \times {10^{ - 34}} \times 5.50 \times {10^{14}} \\
  E = 3.65 \times {10^{ - 19}}J \\
 $
Hence, the energy of a blue light with a wavelength of $545nm$ is $3.65 \times {10^{ - 19}}J$.

Note :
It was discovered that only certain frequencies of light would induce electrons to be ejected. And if the strength of the incident light was very high or it was reflected onto the surface for a long time, no electrons were expelled if the frequency of the incident light was very low (red light, for example).