Question

The frequency of violet light is 7,5 x 1014 Hz.
Find its wavelength in (i) nm, (ii) Å. Speed of
light c = 3 x 10⁸ms-¹​

Answer 1

$\bigstar$ Given

The frequency of violet light is 7.5 x 10¹⁴ Hz

Speed of  light c = 3 x 10⁸ m/s

$\bigstar$ To Find

Find its wavelength in

(i) nm

(ii) Å

$\bigstar$ Solution

We know that

$\purple{\sf \longrightarrow \lambda=\dfrac{c}{v}}$

Here

• λ = wavelength

• c = speed of light

• v = frequency

According to the question

We are asked to find its wavelength

Therefore

We must find "λ"

Given that

The frequency of violet light is 7.5 x 10¹⁴ Hz

Speed of  light c = 3 x 10⁸ m/s

Hence

• v = 7.5 x 10¹⁴ Hz

• c = 3 x 10⁸ m/s

Substituting the values

We get

$\orange{\sf \longrightarrow \lambda=\dfrac{3 \times 10^{8}}{7.5 \times 10^{14}} \ m}$

On further simplification

We get

$\red{\sf \longrightarrow \lambda=0.4 \times 10^{-6} \ m}$

Hence

$\green{\sf \longrightarrow \lambda=4 \times 10^{-7} \ m}$

According to the question

We are asked to find its wavelength in

(i) nm

(ii) Å

We know that

1 nm = 10⁻⁹ m

1 Å = 10⁻¹⁰ m

Therefore

$\blue{\sf (i) \ \lambda= 400 \ nm}$

$\pink{\sf (ii) \ \lambda=4000 \ A^{\circ}}$