Question

In an electron gun, emission current from the cathode is given by the equation,
`I=AT^(2)e^(-(B//(KT)))`[K=Boltzmann constant,A=constant]
The dimensional formula for `AB^(2)` is same as
A. KT
B. `IT^(2)`
C. `IK^(2)`
D. `(IK^(2))/(T)`

Answer 1

`(B)/(KT)` is dimensionless
`therefore [B]=[KT]`
Also `[I]=[AT^(2)]`
`therefore [A]=[T^(-2)]`
`therefore [AB^(2)]=[IK^(2)]`