If the mass of a microscopic particle as well as its speed are halved, the de Broglie wavelength associated with the particle will

Question

If the mass of a microscopic particle as well as its speed are halved, the de Broglie wavelength associated with the particle will (A) increase by a factor more than 2 (B) increase by a factor of 2 (C) decrease by a factor of 2 (D) decrease by a factor more than 2

Tardigrade Admin · Accepted Answer

λ=(h/m v) ∴ (λ2/λ1)=(m1 v1/m2 v2) =(2 m1/m1) (2 v1/v1)=(4/1) ∴ λ2=4 λ1 New wavelength =4 × Original wavelength ∴ The wavelength increases by a factor more than 2 .

Q. If the mass of a microscopic particle as well as its speed are halved, the de Broglie wavelength associated with the particle will

increase by a factor more than 2

increase by a factor of 2

decrease by a factor of 2

decrease by a factor more than 2

$λ = \frac{h}{m v}$
$∴ \frac{λ _{2}}{λ _{1}} = \frac{m _{1} v _{1}}{m _{2} v _{2}}$
$= \frac{2 m _{1}}{m _{1}} \frac{2 v _{1}}{v _{1}} = \frac{4}{1}$
$∴ λ_{2} = 4 λ_{1}$
New wavelength $= 4 \times$ Original wavelength
$∴$ The wavelength increases by a factor more than $2.$

Q. If the mass of a microscopic particle as well as its speed are halved, the de Broglie wavelength associated with the particle will

increase by a factor more than 2

increase by a factor of 2

decrease by a factor of 2

decrease by a factor more than 2

λ=mvh​ ∴λ1​λ2​​=m2​v2​m1​v1​​ =m1​2m1​​v1​2v1​​=14​ ∴λ2​=4λ1​ New wavelength =4× Original wavelength ∴ The wavelength increases by a factor more than 2.

$λ = \frac{h}{m v}$
$∴ \frac{λ _{2}}{λ _{1}} = \frac{m _{1} v _{1}}{m _{2} v _{2}}$
$= \frac{2 m _{1}}{m _{1}} \frac{2 v _{1}}{v _{1}} = \frac{4}{1}$
$∴ λ_{2} = 4 λ_{1}$
New wavelength $= 4 \times$ Original wavelength
$∴$ The wavelength increases by a factor more than $2.$