Question 236: Dual Nature of Matter and Radiation

Question

A beam of electrons of energy E scatters from
a target having atomic spacing of 1 $$\mathop A\limits^o $$. The first
maximum intensity occurs at $$	heta $$ = 60
o
. Then E (in
eV) is ______.
(Planck constant h = 6.64 × 10
–34
Js,
1 eV =
1.6 × 10
–19
J, electron
mass m = 9.1 × 10
–31
kg)

Accepted Answer

Given d = 1 $$\mathop A\limits^o $$
For first maxima, $$	heta $$ = 60
o
$$ 	herefore $$ $$	heta $$
1
= 90 - $${	heta  \over 2}$$
= $$90 - {{60} \over 2}$$ = 60
o
and $$2d\sin 	heta  = \lambda  = {h \over {\sqrt {2mE} }}$$
$$ \Rightarrow $$ $$2 	imes {10^{ - 10}} 	imes {{\sqrt 3 } \over 2} = {{6.6 	imes {{10}^{ - 34}}} \over {\sqrt {2mE} }}$$
$$ \Rightarrow $$ $$E = {1 \over 2} 	imes {{6.64 	imes {{10}^{ - 48}}} \over {9.1 	imes {{10}^{ - 31}} 	imes 3 	imes 1.6 	imes {{10}^{ - 19}}}} = 50.47$$

Dual Nature of Matter and Radiation

A beam of electrons of energy E scatters from a target having atomic spacing of 1 $\mathop A\limits^o . The first maximum intensity occurs at \theta $ = 60 o . Then E (in eV) is ______. (Planck constant h = 6.64 × 10 –34 Js, 1 eV = 1.6 × 10 –19 J, electron mass m = 9.1 × 10 –31 kg)

Integer / Numeric Answer Type