A) \[\lambda =\frac{{{\lambda }_{1}}+{{\lambda }_{2}}}{2}\]
B) \[\frac{2}{\lambda }=\frac{1}{{{\lambda }_{1}}}+\frac{1}{{{\lambda }_{2}}}\]
C) \[\lambda =\sqrt{{{\lambda }_{1}}{{\lambda }_{2}}}\]
D) \[\frac{1}{{{\lambda }^{2}}}=\frac{1}{\lambda _{1}^{2}}+\frac{1}{\lambda _{2}^{2}}\]
Correct Answer: D
Solution :
\[{{\vec{P}}_{1}}=\frac{h}{{{\lambda }_{1}}}\hat{i}\]&\[{{\vec{P}}_{2}}=\frac{h}{{{\lambda }_{2}}}\hat{j}\] Using momentum conservation \[\vec{P}={{\vec{P}}_{1}}+{{\vec{P}}_{2}}\] \[=\frac{h}{{{\lambda }_{1}}}\hat{i}+\frac{h}{{{\lambda }_{2}}}\hat{j}\] \[\left| {\vec{P}} \right|=\sqrt{{{\left( \frac{h}{{{\lambda }_{1}}} \right)}^{2}}+{{\left( \frac{h}{{{\lambda }_{2}}} \right)}^{2}}}\] \[\frac{h}{\lambda }=\sqrt{{{\left( \frac{h}{{{\lambda }_{1}}} \right)}^{2}}+{{\left( \frac{h}{{{\lambda }_{2}}} \right)}^{2}}}\] \[\frac{1}{{{\lambda }^{2}}}=\frac{1}{\lambda _{1}^{2}}+\frac{1}{\lambda _{2}^{2}}\]You need to login to perform this action.
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