Physics Q19 – NEET-UG 2023

Home Physics Dual Nature of MatterQuestion #82

The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of

V

volts is proportional to:

Clue 1 of 3: Energy of X-rays

The maximum energy of an X-ray photon produced is equal to the kinetic energy gained by the electron.

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Ninja Strategy•Fundamental Energy-Wavelength Relationship

Recognize that the energy of the X-ray photon ( $E = h c / λ$ ) comes from the electron's kinetic energy ( $E = e V$ ), implying an inverse relationship between wavelength and potential difference.

🧠 Full Solution Path

Step 1: Relate Electron Energy to Potential Difference✦ Active

When an electron is accelerated through a potential difference $V$ , it gains kinetic energy. The maximum kinetic energy ( $K E_{m a x}$ ) gained by the electron is given by:

K E_{m a x} = e V

where $e$ is the charge of the electron.

Step 2: Relate X-ray Photon Energy to Wavelength○ Expand

When this electron strikes a target, it produces X-rays. The maximum energy of an X-ray photon ( $E_{p h o t o n, m a x}$ ) corresponds to the minimum wavelength ( $λ_{m i n}$ ) and is given by:

E_{p h o t o n, m a x} = h u_{m a x} = \frac{h c}{λ_{m i n}}

where $h$ is Planck's constant and $c$ is the speed of light.

💡 Teacher's Secret Hint

This relationship is fundamental to the photoelectric effect and X-ray production.

Step 3: Determine Proportionality○ Expand

According to the Duane-Hunt law, the maximum kinetic energy of the electron is converted into the maximum energy of the X-ray photon:

e V = \frac{h c}{λ_{m i n}}

Rearranging the equation to find the proportionality of $λ_{m i n}$ :

λ_{m i n} = \frac{h c}{e V}

Since $h$ , $c$ , and $e$ are constants, we can conclude that $λ_{m i n}$ is inversely proportional to the potential difference $V$ .

λ_{m i n} \propto \frac{1}{V}

💡 Teacher's Secret Hint

Remember that $h$ , $c$ , and $e$ are fundamental physical constants.

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Physics Question 19 – NEET-UG 2023

Clue 1 of 3: Energy of X-rays

🧠 Full Solution Path