Question

Violet light has a frequency of 7.26 * 1014 Hz and travels at a speed of 3.00 * 108 m/s.

Answer 1

Answer : The wavelength of violet light is, 413 nm

Explanation :

Formula used :

$\nu=\frac{c}{\lambda}$

where,

$\nu$ = frequency of violet light = $7.26\times 10^{14}Hz=7.26\times 10^{14}s^{-1}$

As we know that, $Hz=s^{-1}$

$\lambda$ = wavelength of violet light

c = speed of light = $3.00\times 10^8m/s$

Now put all the given values in the above formula, we get:

$7.26\times 10^{14}s^{-1}=\frac{3.00\times 10^8m/s}{\lambda}$

$\lambda=\frac{3.00\times 10^8m/s}{7.26\times 10^{14}s^{-1}}$

$\lambda=4.13\times 10^{-7}m=4.13\times 10^{-7}\times 10^9nm=413nm$

conversion used : $1m=10^9nm$

Therefore, the wavelength of violet light is, 413 nm

Answer 2

c=λν

3*10^8 m/s * 10^9 nm/m / 7.26*10^14 s^-1= λ

=413.22 nm

λ=413 nm