The wavelength of X-rays is 0.01 Å . Calculate it's frequency. State the assumption made, if any.

Assumption — Speed of X-rays = 3 x 10⁸ ms^-1

As we know,

Speed of wave (c) = frequency (f) x wavelength (λ)

Given,

c = 3 x 10⁸ ms^-1

λ = 0.01 Å

As 1 Å = 10^-10 m

Hence,

λ = 0.01 Å = 0.01 x 10^-10 m

Substituting the values in the formula above we get,

$3 \times 10^8 = f \times (0.01 \times 10^{-10} ) \\[0.5em] \Rightarrow f = \dfrac{3 \times 10^8}{0.01 \times 10^{-10}} \\[0.5em] \Rightarrow f = \dfrac{3 \times 10^8}{1 \times 10^{-12}} \\[0.5em] \Rightarrow f = 3 \times 10^{20} Hz\\[0.5em]$

Hence,

Frequency of x - rays = 3 x 10²⁰ Hz