The radiation emitted per unit time by unit area of a black body at temperature T is `sigmaT^(4)` wehre `sigma` is the Stefan-Boltzmann constant. The constant `sigma` can also be expressed in terms of Boltmann's constant (k), Planck's constant (h) and speed of light (3) as `sigma=Ak^(alpha)h^(beta)c^(gamma)` where A,`alpha,beta` and `gamma` are dimensionless constants. The set `(alpha,beta,gamma)` is givne by

Options

A. (4,-3,-2)
B. (-4,-3,2)
C. (4,3,2)
D. (-4,-3,-2)

Explanation

(1) Equate dimension /power of M,L, T and q.
`D i m sigma=[sigma]=[MT^(-3)theta^(-4)]`
`[k]=[ML^(2)T^(-2)theta^(-1)]`
`[h]=[ML^(2)T^(-1)]`
`[c]=[LT^(-1)]`
Given:
`q=Ak^(alpha)h^(beta)c^(gamma)`
`[MT^(-3)theta^(-4)]=[ML^(2)T^(-2)theta^(-1)]^(alpha)[ML^(2)T^(-1)]^(beta)[LT^(-1)]^(gamma)`
From `lt1=alpha+beta` ...(i)
From `L,0=2alpha+2beta+gamma` .....(ii
From `T,-3=-2alpha-beta-gamma` ....(iii)
From `theta,-4=-alpha` ......(iv)
From (iv). `alpha=4` ....(v)
From (i) and (v). `beta=-3` ....(vi)
From (ii), (v), (vi) `gamma=-2` ....(vii)
The set `(alpha,beta,gamma)` is (4,-3,-2)