The Question is from NEET guide , and it was created by the author Mr. ANIL KUMAR.G

Question

The energy of a photon is given by $E = h
u$, where $h$ is Planck's constant and $
u$ is the frequency. If a new quantity $X$ is defined as $X = \frac{h^2 
u^3}{E}$, the dimensions of $X$ are:

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [A]
## CONCEPT FRAMEWORK
	**Primary Concept**: Dimensional Analysis
	**Related Topics**: Planck's Constant, Energy of a Photon, Frequency
	**Prerequisites**: Understanding of dimensions of physical quantities, basic algebra
## SOLUTION PATHWAY
**Given Information**:
	*  $E = h
u$
	*  $X = \frac{h^2 
u^3}{E}$
**Method & Steps**:
	1. Substitute the expression for E in the expression for X.
		Reasoning: To simplify the expression for X in terms of h and nu only.
		Formula/Rule: $X = \frac{h^2 
u^3}{E} =  \frac{h^2 
u^3}{h
u}$
	2. Simplify the equation obtained in step 1.
		Working: $X =  \frac{h^2 
u^3}{h
u} = h
u^2$
		Key Point: The expression for X is now in terms of only h and nu.
	3. Determine the dimensions of h and nu.
		Working: Dimensions of h (Planck's constant) are [ML^2T^-1], dimensions of nu (frequency) are [T^-1].
		Key Point: Dimensions of h is [Energy x Time], and energy is [ML^2T^-2], thus [ML^2T^-2 x T] = [ML^2T^-1]. Frequency is inverse of time, hence [T^-1].
	4. Substitute the dimensions of h and nu in the expression for X.
		Working: Dimensions of X = [ML^2T^-1] [T^-1]^2 = [ML^2T^-1] [T^-2] = [ML^2T^-3]
		Key Point: Multiply the dimensions together.
	5. Final result
		Result: Dimensions of X are [ML^2T^-3]
		Verification: The dimensions matches with option A
 ## OPTION ANALYSIS
[A] ✓: The calculated dimensions of X, [ML^2T^-3], match the dimensions given in option A.
[B] :x: The dimensions [MLT^-2] are incorrect. These are the dimensions of force, not the derived quantity X.
[C] :x: The dimensions [M^2L^4T^-5] are incorrect as they do not match with the derived dimensions of X.
[D] :x: The dimensions [ML^3T^-4] are incorrect as they do not match with the derived dimensions of X.
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Incorrectly stating the dimensions of Planck's constant or frequency. [How to avoid]: Memorize or derive the dimensions of fundamental constants and frequency.
		2.[Error 2]: Making mistakes in the algebra while simplifying the expression or dimensions. [How to avoid]: Carefully write out each step and double check the exponents.
	**Quick Tips**:
		1.[Helpful shortcut]: Always simplify the expression before substituting the dimensions.
		2.[Memory aid]: Remember the dimensions of basic quantities like energy, force, frequency and plank's constant to quickly derive other quantities.

Mr. ANIL KUMAR.G · Answer

The correct Option is "[ML^2T^-3]"

Mr. ANIL KUMAR.G · Answer

[MLT^-2]

Mr. ANIL KUMAR.G · Answer

[M^2L^4T^-5]

Mr. ANIL KUMAR.G · Answer

[ML^3T^-4]

NEET Questions

Select Subject

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

NEET Subjects

Our Bots

Company