Answer:
λ = 0.1 nm
E = 2 × 10⁻¹⁵ J
Step-by-step explanation:
Step 1: Given data
Frequency of X-rays (ν): 3 × 10¹⁸ s⁻¹
Step 2: Calculate the wavelength (λ) of a photon of X-rays
We will use the following expression.
c = λ × ν
where,
c: speed of light
λ = c / ν
λ = (3.00 × 10⁸ m/s) / 3 × 10¹⁸ s⁻¹
λ = 1 × 10⁻¹⁰ m × (10⁹ nm/1 m) = 0.1 nm
Step 3: Calculate the energy (E) of a photon of X-rays
We will use the following expression.
E = h × ν
where,
h: Planck's constant
E = 6.63 × 10⁻³⁴ J.s × 3 × 10¹⁸ s⁻¹
E = 2 × 10⁻¹⁵ J