Numford

Modern physicsClass 12, Dual Nature of Radiation and Matter

Dimensional formula of Work function

[M L2 T-2]

Symbolφ0 SI unitjoule (J)

The least energy needed to free an electron from a metal. Often quoted in electron volts.

Derivation

How to get the dimensional formula of work function

  1. Start from the definition: work function = energy.
  2. velocity = length / time, so velocity is [L] / [T] = [L T-1].
  3. energy = mass × velocity2, so energy is [M] × [L T-1]2 = [M L2 T-2].
  4. Put in the dimension of each part: [M L2 T-2].
  5. Add the powers of each base quantity: [M L2 T-2].
Same dimensions

Quantities with the dimensions [M L² T⁻²]

Equal dimensions do not make them the same quantity. Compare work function with the others in the full grid.

Practice

Three questions on work function

1Which of these has the same dimensions as work function?

2What is the SI unit of work function?

3Which one has different dimensions from the others?

Questions

Work function: quick answers

What is the dimensional formula of work function?

The dimensional formula of work function is [M L² T⁻²]. It comes from work function = energy.

What is the SI unit of work function?

The SI unit of work function is the joule (J).

Which quantities have the same dimensions as work function?

Work function shares [M L² T⁻²] with work, energy, kinetic energy, potential energy, torque, torsional constant, gravitational potential energy, strain energy. Equal dimensions do not make them the same quantity.

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