Correct Answer - Option 3 : 0.024 Å

**Concept:**

**Compton effect:**

- Compton effect is the term used for an
** unusual result observed** when** X-rays **are** scattered** on some materials.
- During the study, Compton found that
**wavelength **is** not dependent** on the **intensity** of incident radiation.
- It is
**dependent** on the **angle of scattering and** on the wavelength of the incident beam.

Mathematically,

\( λ'-λ=\frac{h}{m_0c}\left(1-cosϕ\right)\)

Where,

λ' = Wavelength after & Scattering,

λ = initial wavelength,

mo = rest mass of an electron = 9.109 × 10^{−31 }kg,

c = speed of light = 3 × 10^{8} m/s,

h = Planck's constant = 6.626×10^{−34} joule-sec,

ϕ = angle at which radiation scattered.

**Calculation:**

We know that,

\( λ'-λ=\frac{h}{m_0c}\left(1-cosϕ\right)\)

Given,

ϕ = 90∘

\(⇒ Δ λ = \frac{6.626\times 10^-34}{9.1\times 106-31 \times 3 \times 10^8}(1 - cos90^\circ )\)

⇒ Δλ = 0.024 Å

Hence, the **wavelength** will be ** 0.024 Å.**