The dimensions of Stefan-Boltzman constant `sigma` can be written in terms of Plank's constant h. Boltzmann constant `k_(B)` and the speed of light c as `sigma = h^(alpha) K_(B)^(b) c^(Y)`. Here

Options

A. `alpha = 3,beta = 4 and gamma = -3`
B. `alpha = 3,beta = -4 and gamma = 2`
C. `alpha = -3,beta = 4 and gamma = -2`
D. `alpha = 2,beta = -3 and gamma = -1`

Answer

C

Explanation

`sigma=h^(alpha)k_B^(beta)c^(gamma)`
`implies [M^1L^0 T^(-3)K^(-4)]=[M^1L^2T^(-1)]^(alpha)[ML^2 T^(-2)K^(-1)]^(beta) [LT^(-1)]^(gamma)`
`alpha +beta =1`
`2 alpha + 2beta + gamma =0`
`-alpha -2beta - gamma =-3`
`-beta = -4 implies beta =4`
`alpha = -3 and gamma =-2`