Question 177: Dual Nature of Matter and Radiation

Question

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :

Accepted Answer

Given, V = 1.24 million volt = 1.24 $$	imes$$ 10
6
volt
Since, energy (E) = eV
where, e is the charge of electron = 1.6 $$	imes$$ 10
$$-$$19
C
$$	herefore$$ E = 1.6 $$	imes$$ 10
$$-$$19
$$	imes$$ 1.24 $$	imes$$ 10
6
..... (i)
As we know that,
Energy of photon, $$E = {{hc} \over \lambda }$$ .... (ii)
Here, Planck's constant, h = 6.67 $$	imes$$ 10
$$-$$34
J-s,
c = speed of light in free space, c = 3 $$	imes$$ 10
8
ms
$$-$$1
Equating Eqs. (i) and (ii), we get
$$1.6 	imes {10^{ - 19}} 	imes 1.24 	imes {10^6} = {{6.67 	imes {{10}^{ - 34}} 	imes 3 	imes {{10}^8}} \over \lambda }$$
$$ \Rightarrow \lambda  = {{20.01 	imes {{10}^{ - 13}}} \over {1.6 	imes 1.24}} = 10.09 	imes {10^{ - 13}}$$
$$ = 1.009 	imes {10^{ - 12}} \simeq {10^{ - 3}} 	imes {10^{ - 9}}$$
= 10
$$-$$3
nm

Answer

10$$-$$2 nm

Answer

10$$-$$1 nm

Answer

10$$-$$3 nm

Answer

10$$-$$4 nm

Dual Nature of Matter and Radiation

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :

Choose the correct answer: