Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
The Special Theory of Relativity

Concepts Of Physics MCQ Edition [Volume 2] · Physics · The Special Theory of Relativity

Determine the speed of an electron possessing a kinetic energy of 1...

Determine the speed of an electron possessing a kinetic energy of 1 eV1 \text{ eV}.

Options

  1. A8.37×105 m s−18.37 \times 10^{5} \text{ m s}^{-1}
  2. B5.92×105 m s−15.92 \times 10^{5} \text{ m s}^{-1}
  3. C4.19×105 m s−14.19 \times 10^{5} \text{ m s}^{-1}
  4. D5.92×107 m s−15.92 \times 10^{7} \text{ m s}^{-1}

Correct answer

B. 5.92×105 m s−15.92 \times 10^{5} \text{ m s}^{-1}

Step-by-step solution

The kinetic energy of the electron is given as K=1 eVK = 1 \text{ eV}.

Converting to Joules:

K=1.6×10−19 JK = 1.6 \times 10^{-19} \text{ J}

The mass of an electron is m=9.1×10−31 kgm = 9.1 \times 10^{-31} \text{ kg}.

Using the formula for kinetic energy K=12mv2K = \dfrac{1}{2} m v^2, the speed vv is:

v=2Kmv = \sqrt{\dfrac{2K}{m}}

Substituting the values:

v=2×1.6×10−199.1×10−31v = \sqrt{\dfrac{2 \times 1.6 \times 10^{-19}}{9.1 \times 10^{-31}}}

v=3.29.1×1012v = \sqrt{\dfrac{3.2}{9.1} \times 10^{12}}

v=0.3516×1012v = \sqrt{0.3516 \times 10^{12}}

v≈0.593×106 m s−1=5.93×105 m s−1v \approx 0.593 \times 10^{6} \text{ m s}^{-1} = 5.93 \times 10^{5} \text{ m s}^{-1}

The closest value among the options is 5.92×105 m s−15.92 \times 10^{5} \text{ m s}^{-1}.
Practice The Special Theory of Relativity on Quantrex Academy →

More from The Special Theory of Relativity

A yogi's guru resides in a Karakoram cave, located 1000 km away from the house of the… Concepts Of Physics MCQ Edition [Volume 2]Measured at rest, a rod has an exact length of 1 m . Determine its length when it travels… Concepts Of Physics MCQ Edition [Volume 2]Measured at rest, a rod has an exact length of 1 m . Determine its length when it travels… Concepts Of Physics MCQ Edition [Volume 2]Measured at rest, a rod has an exact length of 1 m . Determine its length when it travels… Concepts Of Physics MCQ Edition [Volume 2]A shop owner measures a suitcase kept on a rack to be 50 cm × 25 cm × 10 cm . A traveller… Concepts Of Physics MCQ Edition [Volume 2]A shop owner measures a suitcase kept on a rack to be 50 cm × 25 cm × 10 cm . A traveller… Concepts Of Physics MCQ Edition [Volume 2]A person standing on a platform notes that a train travelling with a velocity of 0.6c… Concepts Of Physics MCQ Edition [Volume 2]A person standing on a platform notes that a train travelling with a velocity of 0.6c… Concepts Of Physics MCQ Edition [Volume 2] Full The Special Theory of Relativity list All Concepts Of Physics MCQ Edition [Volume 2] PYQs