| Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature. |
| Reason (R): The root mean square velocity of gas molecules depends on temperature. |
A) Both A and R are true and R is the correct explanation of A
B) Both A and R are true but R is NOT the correct explanation of A
C) A is true but R is false
D) A is false and R is true
Correct Answer: A
Solution :
| Option [a] is correct |
| Explanation: \[{{v}_{\operatorname{RMS}}}=\sqrt{\frac{3RT}{M}}\] |
| So, \[{{v}_{\operatorname{RMS}}}\propto \surd \operatorname{T}\] |
| Again de-Broglie wavelength, \[\lambda =h/mv\] |
| So, \[\lambda \propto 1/\surd T\] |
| Hence, assertion and reason both are true and reason explains the assertion. |
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