Question

In an atomic bomb, the temperature of $10$ million degrees is developed at the moment of explosion. In what region of the spectrum do the wavelength corresponding to maximum energy density lie?

($b=0.28$ x ${10}^{-2}S.I.unit$)

• A. ultra-violet
• B. visible
• C. infra-red rays
• D. x-rays

Answer 1

The correct option is D x-rays

From Wien's displacement Law, ${\lambda }_{m}T=b$

where ${\lambda }_m$ is the wavelength at which energy density is maximum, T is the temperature in absolute scale and b is a constant (given).

$b=0.28\ast {10}^{-2}$

$T=10\times {10}^6$${}^{\circ }C$

$T={10}^7+273$ in K

${\lambda }_m=\frac{b}{T}=\frac{0.28\times {10}^{-2}}{{10}^7+273}=0.28\ast {10}^{-9}$

We have approximated ${10}^7+273={10}^7$
The wavelength falls in the x-ray range.