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Rahul Gupta asked in Physics

Check correctness of relation by dimensional analysis lambda =h/mv where letter have heir own usual meaning?

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A K Daya Sir answered this
3668 helpful votes in Physics, Class XI-Science

λ = h/mv [de-Broglie wavelength]

From E = hv [Plank's equation]

h = E/v

Write the dimension of each quantity in the above relation

λ = wavelength = [L] ,

h = Energy / frequency = Energy x time = [ML2 T-2 ][T] = [ML2 T-1 ]

mv = mass x velocity = momentum = [MLT-1]

--

LHS = [L]

RHS = [ML2 T-1 ] / [MLT-1 ] = [L]

We see that dimensions of both sides are equal to [L]

The given relation is correct.

Answer 1

The given relation is absolutely correct.

• λ = h/mv [de-Broglie wavelength]
• E = hv [Plank's equation]
• h = E/v
• Writing the dimension of each quantity in the above relation
• λ = wavelength = [L] ,
• h = Energy / frequency = Energy x time = [ML2 T-2 ][T] = [ML2 T-1 ]
• mv = mass x velocity = momentum = [MLT-1]
• LHS = [L]
• RHS = [ML2 T-1 ] / [MLT-1 ] = [L]
• dimensions of both sides are equal to [L]
• The given relation is correct.

Answer 2

The given relation is correct, LHS = RHS

• Here lambda is wavelength and and  h is the plancks constant

• λ = h/mv
• E = hν
• h = E/ν = hc/λ/ν
• where ν is frequency , c speed of light and λ is wavelength m is mass and v is velocity , product of mv is also known as momentum
• unit of λ is meter, and its dimension will be kenght = M⁰L¹T⁰
• h = Eenergy× time = M¹L²T⁻¹, where unit of frequency is inverse of time
• mv is momentum = M¹L¹T⁻¹
• Now here dimensions of both sides are equal and hence LHS = RHS
• The above relation is correct

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