An electron is travelling with a velocity v in free space and when it enters a medium, its velocity is reduced by 20 % . The de Broglie wavelength of electron in the medium is ₀ , where ₀ is its de Broglie wavelength in free space. The value of is _______.

Step-by-step solution

The de Broglie wavelength of an electron in free space is given by ₀ = h mv . When the electron enters the medium, its velocity is reduced by 20 % . The new velocity is v' = v - 0.20v = 0.80v . The de Broglie wavelength in the medium is ' = h mv' . Substituting v' = 0.80v , we get ' = h m(0.80v) = 1 0.80 ( h mv ) . Since 1 0.80 = 100 80 = 1.25 , we have ' = 1.25 ₀ . Comparing this with ' = ₀ , we get = 1.25 . Answer: 1.25