Question

Violet light has a frequency of 7.26 × 10^14 Hz and travels at a speed of 3.00 × 10^8 m/s. HINT: to convert to nanometers (nm) multiply your final answer by 10^9. *
1 point
Captionless Image
2.18 x 10^32 nm
413 nm
2.42 x10^15
0.00242

Answer 1

Answer:

413 nm

Explanation:

The wavelength is defined as

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

Where $\lambda$ represents the wavelength, $c$ the speed of the wave which is a constant and $f$ is the frequency of the wave,

In this case, we know

$c = 3.00 \times 10^{8} m/s$

$f=7.26 \times 10^{14}Hz$, where $Hz=\frac{1}{sec}$

Replacing these given values in the formula, we have

$\lambda= \frac{3.00 \times 10^{8} m/s }{7.26\times 10^{14} \frac{1}{sec} }\\ \lambda = 0.4132 \times 10^{-6} m$

But, we know that $1 \ m = 10^{9} \ nm$

So, we use the equivalence to transform the wavelength from meters to nanometers.

$0.4132 \times 10^{-6}m\frac{10^{9}nm }{1m} =0.4132 \times 10^{3} \ nm=413.2 nm$

Therefore, the wavelength is 413.2 nanometers, approximately.