Calculate the mass of a hypothetical particle having wavelength 5894 A

1.	Calculate the mass of a hypothetical particle having wavelength 5894 A and velocity 1.0 × 108 ms-1.
Answer» Given : Wavelength (λ) = 5894 Å, Velocity (ν) = 1.0 × 10⁸ ms^-1 To find : Mass of a particle Formula : λ = \(\frac{h}{mv}\) or m = \(\frac{h}{\lambda v}\) (according to de-Broglie equation) Calculation : m = \(\frac{h}{\lambda v}\) ∴ m = \(\frac{6.626\times 10^{-34}kg\,m^2s^{-1}}{(5894\times 10^{-10}m)\times (1.0\times 10^8 ms^{-1})}\) = 1.124 × 10^-35 kg Mass of a particle is 1.124 × 10^-35 kg. [Calculation using log table : \(\frac{6.626\times 10^{-34}}{5894\times 10^{-10}\times 1.0\times 10^8}\) = \(\frac{6.626}{5894}\) x 10^-32 = Antilog₁₀[log₁₀6.626 – log₁₀5894] × 10^-32 = Antilog₁₀[0.8213 – 3.7704] × 10^-32 = Antilog₁₀ \(\overline{3} .0509\) x 10^-32 = 1.124 × 10^-35]

Calculate the mass of a hypothetical particle having wavelength 5894 A and velocity 1.0 × 108 ms-1.

Answer»

Given :

Wavelength (λ) = 5894 Å,

Velocity (ν) = 1.0 × 10⁸ ms^-1

To find :

Mass of a particle

Formula :

λ = \(\frac{h}{mv}\) or m = \(\frac{h}{\lambda v}\)

(according to de-Broglie equation)

Calculation :

m = \(\frac{h}{\lambda v}\)

∴ m = \(\frac{6.626\times 10^{-34}kg\,m^2s^{-1}}{(5894\times 10^{-10}m)\times (1.0\times 10^8 ms^{-1})}\)

= 1.124 × 10^-35 kg

Mass of a particle is 1.124 × 10^-35 kg.

[Calculation using log table :

\(\frac{6.626\times 10^{-34}}{5894\times 10^{-10}\times 1.0\times 10^8}\)

= \(\frac{6.626}{5894}\) x 10^-32

= Antilog₁₀[log₁₀6.626 – log₁₀5894] × 10^-32

= Antilog₁₀[0.8213 – 3.7704] × 10^-32

= Antilog₁₀ \(\overline{3} .0509\) x 10^-32

= 1.124 × 10^-35]