20. A photon of X -rays of (wavelength $$ =7 \mathrm{~A}^{\circ} $$ ) collides a stationary electron, the energy of the electron after collision is $$ 1.853 imes 10^{\wedge}(-18) \mathrm{J} $$ the wavelength of the photon after collision is...... $$ \mathrm{A}^{\circ} $$. 7.46 7.046 8.2

Question

20. A photon of X -rays of (wavelength $$ =7 \mathrm{~A}^{\circ} $$ ) collides a stationary electron, the energy of the electron after collision is $$ 1.853 	imes 10^{\wedge}(-18) \mathrm{J} $$ the wavelength of the photon after collision is...... $$ \mathrm{A}^{\circ} $$. 7.46 7.046 8.2

UpStudy AI · Accepted Answer

**Step 1. Calculate the Initial Photon Energy**

The energy of a photon is given by

$$
E = \frac{hc}{\lambda}
$$

where  
$$ h = 6.626 \times 10^{-34} \, \mathrm{Js} $$ (Planck's constant),  
$$ c = 3.00 \times 10^{8} \, \mathrm{m/s} $$ (speed of light),  
$$ \lambda = 7 \, \mathrm{\AA} = 7 \times 10^{-10} \, \mathrm{m} $$.

Thus, the initial photon energy is

$$
E_i = \frac{(6.626 \times 10^{-34})(3.00 \times 10^8)}{7 \times 10^{-10}}.
$$

Calculating the numerator:

$$
6.626 \times 10^{-34} \times 3.00 \times 10^{8} = 1.9878 \times 10^{-25} \, \mathrm{J \cdot m}.
$$

Then

$$
E_i = \frac{1.9878 \times 10^{-25}}{7 \times 10^{-10}} \approx 2.8397 \times 10^{-16} \, \mathrm{J}.
$$

**Step 2. Determine the Energy Left for the Photon After Collision**

By energy conservation, the energy lost by the photon is gained by the electron. We are told that the electron gains an energy of

$$
K_e = 1.853 \times 10^{-18} \, \mathrm{J}.
$$

Thus, the energy of the photon after collision is

$$
E_f = E_i - K_e \approx 2.8397 \times 10^{-16} \, \mathrm{J} - 1.853 \times 10^{-18} \, \mathrm{J} \approx 2.8212 \times 10^{-16} \, \mathrm{J}.
$$

**Step 3. Find the Final Wavelength of the Photon**

Using the photon energy relation again for the photon after collision:

$$
\lambda' = \frac{hc}{E_f}.
$$

Substituting the values:

$$
\lambda' = \frac{1.9878 \times 10^{-25} \, \mathrm{J \cdot m}}{2.8212 \times 10^{-16} \, \mathrm{J}} \approx 7.05 \times 10^{-10} \, \mathrm{m}.
$$

Since

$$
1 \, \mathrm{\AA} = 10^{-10} \, \mathrm{m},
$$

we have

$$
\lambda' \approx 7.05 \, \mathrm{\AA}.
$$

Comparing with the available options, the closest value is

$$
7.046 \, \mathrm{\AA}.
$$
The wavelength of the photon after collision is approximately $$ 7.046 \, \mathrm{\AA} $$.

A photon of X -rays of (wavelength ) collides a stationary electron, the energy of the electron after collision is the wavelength of the photon after collision is… .
7.46
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8.2

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A photon of X -rays of (wavelength ) collides a stationary electron, the energy of the electron after collision is the wavelength of the photon after collision is… . 7.46 7.046 8.2