Question

An X-ray photon of wavelength 0.3 Aº is scattered through
an angle of 45° by by a loosely bound electron find wavelength of scattered photon.
​

Answer 1

Step-by-step explanation:

Given: incident wavelength ( $\lambda$ ) = $0.3 \ A^{o}$

scattered angle ( $\theta$ ) = $45^{o}$

To Find: wavelength of scattered photon ( $\lambda^{'}$ )

Solution:

• Calculating the wavelength of the scattered photon ( $\lambda^{'}$ )

In Compton scattering, the wavelength of the scattered photon is calculated as;

$\lambda^{'} - \lambda = \frac{h}{m_{0}c} (1-cos(\theta))$

where the quantity $\frac{h}{m_{0}c}$ is called the Compton wavelength $\lambda_{c}$ having a value of $0.0242 \ A^{o}$

Therefore, we can calculate  $\lambda^{'}$ as;

$\Rightarrow \lambda^{'} - \lambda = \frac{h}{m_{0}c} (1-cos(\theta))$

$\Rightarrow \lambda^{'} - 0.3 = 0.0242 (1-cos(45^{o} ))$

$\Rightarrow \lambda^{'} = 0.3 + 0.0071 = 0.3071 \ A^{o}$

Hence, the wavelength of the scattered x-ray photon is $\lambda^{'} = 0.3071 \ A^{o}$

Answer 2

Answer:

 The wavelength of the scattered x-ray photon is 0.3071A°

Step-by-step explanation:

• In context to  the given question; we have to find the wavelength of scattered photon

• Given: incident wavelength (λ) = 0.3 A°
• scattered angle (θ) = 45°

Let the wavelength of scattered photon be ( λ₁)

We know that,

In Compton scattering, the wavelength of the scattered photon is calculated as;

λ₁ - λ = [h/ m₀ c] ( 1 - cos θ )

where;

[h/ m₀ c] =  Compton wavelength  = 0.0242 A°

By putting the known values we get

⇒ λ₁ - λ = [h/ m₀ c] ( 1 - cos θ )

⇒  λ₁ - 0.3 = 0.0242 ( 1 - cos45° )

⇒  λ₁ - 0.3 = 0.0242 ( 1 - 0.7071 )           [cos45° = 0.7071 ]

⇒  λ₁ - 0.3 = 0.0242 (0.2929 )  

⇒  λ₁ - 0.3 = 0.00708

⇒  λ₁ = 0.00708 + 0.3

⇒  λ₁ = 0.30708 A° ≅ 0.3071A°

Hence,

The wavelength of the scattered x-ray photon is 0.3071A°