Calculate the mass of a hypothetical particle having wavelength 5894 A and velocity 1.0 × 10^8 ms^(-1).

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]