Question

Kinetic energy of proton accelerated under p.d. \(1 \mathrm{~V}\) will be........ (A) \(1840 \mathrm{eV}\) (B) \(13.6 \mathrm{eV}\) (C) \(1 \mathrm{eV}\) (D) \(0.54 \mathrm{eV}\)

Short answer

The kinetic energy of a proton accelerated under a potential difference (p.d.) of \(1 \text{V}\) is \(1 \text{eV}\).

Step-by-step solution

1. Write down the given information and constants.

We are given: - Potential Difference (p.d.): \(V = 1\,\text{V}\) - Charge of a proton: \(q_p = 1.6 \times 10^{-19}\,\text{C}\) - Mass of a proton: \(m_p = 1.67 \times 10^{-27}\,\text{kg}\) 1 electron volt: \(\text{1 eV} = 1.6 \times 10^{-19} \,\text{J}\)

2. Calculate the work done on the proton by the electric field.

We can use the potential difference and the proton's charge to calculate the amount of work the electric field does on the proton: Work Done = \(q_p \times V\) Work Done = \((1.6 \times 10^{-19}\,\text{C}) \times (1\,\text{V})\) Work Done = \(1.6 \times 10^{-19}\,\text{J}\)

3. Determine the kinetic energy of the proton.

Since all the work done on the proton is converted into its kinetic energy, we can write: Kinetic Energy = Work Done Kinetic Energy = \(1.6 \times 10^{-19}\,\text{J}\)

4. Convert the kinetic energy to electron volts.

To convert the kinetic energy to eV, we can use the definition of 1 eV: Kinetic Energy in eV = \(\frac{1.6 \times 10^{-19}\,\text{J}}{1.6 \times 10^{-19} \,\text{J/eV}}\) Kinetic Energy in eV = \(1\,\text{eV}\) So the answer is: (C) \(1\,\text{eV}\)