Question

what happens to the energy of a photon if the wavelength is doubled? answer: a energy doubles. b energy quadruples. c there is no change in energy. d energy is reduced by one - half. e energy is reduced by one - quarter.

Explanation:

Step1: Recall the energy - wavelength formula

The energy of a photon is given by \(E = h
u\), and since \(
u=\frac{c}{\lambda}\) (where \(h\) is Planck's constant, \(c\) is the speed of light, \(
u\) is the frequency and \(\lambda\) is the wavelength), we can rewrite the energy formula as \(E=\frac{hc}{\lambda}\).

Step2: Analyze the effect of doubling the wavelength

Let the initial wavelength be \(\lambda_1=\lambda\) and the initial energy be \(E_1 = \frac{hc}{\lambda}\). When the wavelength is doubled, \(\lambda_2 = 2\lambda\). Then the new energy \(E_2=\frac{hc}{\lambda_2}=\frac{hc}{2\lambda}\).

Step3: Compare \(E_1\) and \(E_2\)

We can see that \(E_2=\frac{1}{2}E_1\)

Answer:

D. Energy is reduced by one - half.