Question

^{Determine the amount of time it takes for X-rays of frequency$\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{18}}\mathbf{}\mathbf{Hz}$to travel (a) 1 mm and (b) 1 cm}

Short answer

1. The time taken for 1mm is $3.34\times {10}^{-12}s$.

b. The time taken for 1cm is $3.34\times {10}^{-11}s$.

Step-by-step solution

Definition of frequency

The number of waves that travel through a particular point in a given amount of time is referred to as frequency.

Given information and Formula to be used

$$\begin{gathered} \mathrm{f}=3\times {10}^{18}\mathrm{Hz} \\ \mathrm{c}=3\times {10}^{18}\mathrm{m}/\mathrm{s} \\ \mathrm{d}=1\mathrm{mm}\left(\frac{{10}^{-3}\mathrm{m}}{1\mathrm{mm}}\right)={10}^{-3}\mathrm{m} \\ \mathrm{d}=1\mathrm{cm}\left(\frac{{10}^{-2}\mathrm{m}}{1\mathrm{cm}}\right)={10}^{-2}\mathrm{m} \end{gathered}$$

Distance is \(d = ct\) ……………(1)

Calculate the amount of time it takes for X-rays of frequency 3×1018 Hz travel 1mm ?

a)

Substitute the given data in equation (1), and we get,

$$\begin{gathered} {10}^{-3}\mathrm{m}=\left(3\times {10}^8\mathrm{m}/\mathrm{s}\right)\times \mathrm{t} \\ \mathrm{t}=\frac{{10}^{-3}\mathrm{m}}{3\times {10}^8\mathrm{m}/\mathrm{s}} \\ \mathrm{t}=3.34\times {10}^{-12}\mathrm{s} \end{gathered}$$

Therefore, the time taken is $3.34\times {10}^{-12}s$.

Calculate the amount of time it takes for X-rays of frequency 3×1018 Hz travel 1 cm ? 

b)

Substitute the given data in equation (1), and we get,

$$\begin{gathered} {10}^{-2}\mathrm{m}=\left(3\times {10}^8\mathrm{m}/\mathrm{s}\right)\times \mathrm{t} \\ \mathrm{t}=\frac{{10}^{-2}\mathrm{m}}{3\times {10}^8\mathrm{m}/\mathrm{s}} \\ \mathrm{t}=3.34\times {10}^{-11}\mathrm{s} \end{gathered}$$

Therefore, the time taken is$3.34\times {10}^{-11}\mathrm{s}$ .