1Which of these has the same dimensions as activity?
Activity and velocity gradient both have the dimensions [T⁻¹].
Modern physicsClass 12, Nuclei
Dimensional formula of Activity
[T-1]
Decays per second, R = λN. The number of nuclei has no dimension.
How to get the dimensional formula of activity
- Start from the definition: activity = decay constant.
- decay constant = 1 / time, so decay constant is 1 / [T] = [T-1].
- Put in the dimension of each part: [T-1].
- Add the powers of each base quantity: [T-1].
Quantities with the dimensions [T⁻¹]
Equal dimensions do not make them the same quantity. Compare activity with the others in the full grid.
Three questions on activity
2What is the SI unit of activity?
The SI unit of activity is the becquerel (Bq).
3Which one has different dimensions from the others?
Stopping potential is [M L² T⁻³ A⁻¹]. The other three are all [T⁻¹].
Activity: quick answers
What is the dimensional formula of activity?
The dimensional formula of activity is [T⁻¹]. It comes from activity = decay constant.
What is the SI unit of activity?
The SI unit of activity is the becquerel (Bq).
Which quantities have the same dimensions as activity?
Activity shares [T⁻¹] with angular velocity, velocity gradient, frequency, angular frequency, decay constant. Equal dimensions do not make them the same quantity.