Question

Calculate the maximum energy in eV, that can be transferred to an electron in a Compton
experiment when the incident quanta are X-rays of wavelength 0.50 Å.​

Answer 1

1. 13263t46455333664rdf7r

1.00 A

Answer 2

The maximum energy to be transferred to an electron is 2.133 KeV

Step-by-step Explanation:

Given: wavelength λ = 0.50 Å

To Find: The maximum energy to be transferred to an electron

Solution:

• Finding the maximum energy to be transferred to an electron

For the Compton scattering effect, the energy E for the electron with rest mass $m_o$, incident frequency $\nu$, and the incident angle $\theta$ is given as;

$E = h \nu \Big( \frac{\alpha(1-cos\theta)}{1+\alpha(1-cos\theta)} \Big) \ \cdots \cdots (1)$

where $\alpha = \frac{h \nu}{m_o c^{2} }$

Using the relation between frequency and wavelength, we have

$\nu = \frac{c}{\lambda} \Rightarrow \nu = \frac{3 \times 10^8}{0.5 \times 10^{-10}} = 6 \times 10^{18} \ \cdots \cdots (2)$

And, $\alpha = \frac{6.6 \times 10^{-34} \times 6 \times 10^{18} \nu}{9.1 \times 10^{-31} (3 \times 10^{8})^{2} } = 0.048352 \ \cdots \cdots (3)$

Since we have to find the maximum energy, therefore the angle $\theta = 180^o$

Also, substituting the values (2) and (3) in (1), we get;

$\Rightarrow E = (39.6 \times 10^{-16}) \Big( \frac{(0.048352)(1-cos180^o)}{1+(0.048352)(1-cos180^o)} \Big)$

$\Rightarrow E = (39.6 \times 10^{-16}) \Big( \frac{0.096704}{1.096704} \Big)$

$\Rightarrow E = 3.418092 \times 10^{-16} \ J$

To find the energy in eV, we have $1J = 6.242 \times 10^{18} eV$

Therefore, $E = 2133.405 \ eV = 2.133 \ KeV$

Hence, the maximum energy to be transferred to an electron in a Compton experiment  is 2.133 KeV