
Assertion : The de - Broglie wavelength of a molecule varies inversely as the square root of temperature. Reason : The root mean square velocity of the molecule depends on the temperature.
A. If both assertion and reason are true and reason is the correct explanation of the assertion.
B. If both assertion and reason are true but reason is not the correct explanation of the assertion.
C. If the assertion is true but the reason is false.
D. If both the assertion and reason are false.
Answer
161.4k+ views
Hint:In order to solve this question, we will first write the formula of De- Broglie wavelength and then we will check whether the assertion and reason are correct statements or not and also the correctness of reason for the given assertion.
Formula used:
The de- Broglie wavelength is given as,
$\lambda = \dfrac{h}{{mv}}$
where, h is Plank’s constant, m is the mass, and v is the velocity of the molecule.
The expression for root mean square velocity is,
${v_{r.m.s}} = \sqrt {\dfrac{{3kT}}{m}} $
Here, $m$ is the mass, $T$ is the temperature and $k$ is the boltzmann constant.
Complete step by step solution:
As we know that, the de- Broglie wavelength is given by the formula as,
$\lambda = \dfrac{h}{{mv}}$
We also know that for a molecule of a gas its velocity is directly proportional to the temperature is,
${v_{r.m.s}} = \sqrt {\dfrac{{3kT}}{m}} $
Using this, the de- Broglie wavelength will depend upon temperature as $\lambda \propto \dfrac{h}{{m\sqrt T }}$
So, our assertion: The de - Broglie wavelength of a molecule varies inversely as the square root of temperature is correct as we found $\lambda \propto \dfrac{h}{{m\sqrt T }}$
And our reason: The root mean square velocity of the molecule depends on the temperature is also correct as $v \propto \sqrt T $ and also reason is not the correct explanation of our assertion because reason does not provide how the velocity depends upon temperature
Hence, the correct answer is option B.
Note: It should be remembered that the de-Broglie wavelength is the wavelength associated with every matter in the universe and this concept shows the wave nature of matter apart from the particle nature of matter.
Formula used:
The de- Broglie wavelength is given as,
$\lambda = \dfrac{h}{{mv}}$
where, h is Plank’s constant, m is the mass, and v is the velocity of the molecule.
The expression for root mean square velocity is,
${v_{r.m.s}} = \sqrt {\dfrac{{3kT}}{m}} $
Here, $m$ is the mass, $T$ is the temperature and $k$ is the boltzmann constant.
Complete step by step solution:
As we know that, the de- Broglie wavelength is given by the formula as,
$\lambda = \dfrac{h}{{mv}}$
We also know that for a molecule of a gas its velocity is directly proportional to the temperature is,
${v_{r.m.s}} = \sqrt {\dfrac{{3kT}}{m}} $
Using this, the de- Broglie wavelength will depend upon temperature as $\lambda \propto \dfrac{h}{{m\sqrt T }}$
So, our assertion: The de - Broglie wavelength of a molecule varies inversely as the square root of temperature is correct as we found $\lambda \propto \dfrac{h}{{m\sqrt T }}$
And our reason: The root mean square velocity of the molecule depends on the temperature is also correct as $v \propto \sqrt T $ and also reason is not the correct explanation of our assertion because reason does not provide how the velocity depends upon temperature
Hence, the correct answer is option B.
Note: It should be remembered that the de-Broglie wavelength is the wavelength associated with every matter in the universe and this concept shows the wave nature of matter apart from the particle nature of matter.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

Young's Double Slit Experiment Step by Step Derivation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

JEE Isolation, Preparation and Properties of Non-metals Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Wheatstone Bridge for JEE Main Physics 2025

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

Uniform Acceleration

Degree of Dissociation and Its Formula With Solved Example for JEE
