Question

Choose the correct values of wavelength and frequency of a light wave whose time period is $2\times {10}^{-10}s$.

• A. Frequency = $5\times {10}^9{s}^{-1}$,
  wavelength = $6\times {10}^{-2}m$
• B. Frequency = $5\times {10}^9{s}^{-1}$,
  wavelength = $2\times {10}^{-2}m$
• C. Frequency = $1.67\times {10}^9{s}^{-1}$,
  wavelength =$6\times {10}^{-2}m$
• D. Frequency = $5\times {10}^3{s}^{-1}$,
  wavelength =$6\times {10}^{-2}m$

Answer 1

The correct option is A Frequency = $5\times {10}^9{s}^{-1}$,

wavelength = $6\times {10}^{-2}m$
Given: Time period = $2\times {10}^{-10}s$
Now, frequency $=\frac{1}{\text{time period}}=\frac{1}{2\times {10}^{-10}s}=5\times {10}^9{s}^{-1}$.

Using relation between wavelength and frequency: $\lambda =\frac{c}{v}$
where,
$\lambda$= wavelength of the radiation
c = speed of light
v = frequency of the wave

$\lambda =\frac{3\times {10}^8}{5\times {10}^9}=6\times {10}^{-2}m$