6.Calculate the wavelength of de Broglie waves associated with a proto

1.	6.Calculate the wavelength of de Broglie waves associated with a proton of kinetic energy500 ev? (Given; mp=1.67x10-27 kg, h-6.63x10."js)
Answer» Convert the KE from eV to Joule. 1eV=1.6⋅10^−19J 500eV=500×1.6⋅10^−19 = 8×10^-17J While the mass of proton is well defined, we must find its velocity. m = 1.67×10^-27 kg KE = 8×10^-17 J KE = 1/2×m×v^2 v^2 = KE/0.5×m v = (KE/0.5×m)^1/2 v = (8×10^-17/(0.5×1.67×10^-27))^1/2 v = (16/1.67)^1/2 × 10^5 = 2.4 × 10^5 m/s The momentum is given as:p= m×v = 1.67×10^-27 × 2.4×10^5 = 4 × 10^-22 kg. m/s While the Plack constant is defined, the De Broglie wavelength is given as: λ = h/p h = 6.63 × 10^-34 m^2⋅kg/s(Planck constant) λ = 6.63 × 10^-34/4 × 10^-22 m The De Broglie wavelength of proton with 500 eV kinetic energy is: λ = 1.657 × 10^-12 m

6.Calculate the wavelength of de Broglie waves associated with a proton of kinetic energy500 ev? (Given; mp=1.67x10-27 kg, h-6.63x10."js)

Answer»

Convert the KE from eV to Joule.

1eV=1.6⋅10^−19J

500eV=500×1.6⋅10^−19 = 8×10^-17J

While the mass of proton is well defined, we must find its velocity.

m = 1.67×10^-27 kg

KE = 8×10^-17 J

KE = 1/2×m×v^2

v^2 = KE/0.5×m

v = (KE/0.5×m)^1/2

v = (8×10^-17/(0.5×1.67×10^-27))^1/2

v = (16/1.67)^1/2 × 10^5 = 2.4 × 10^5 m/s

The momentum is given as:p= m×v = 1.67×10^-27 × 2.4×10^5 = 4 × 10^-22 kg. m/s

While the Plack constant is defined, the De Broglie wavelength is given as:

λ = h/p

h = 6.63 × 10^-34 m^2⋅kg/s(Planck constant)

λ = 6.63 × 10^-34/4 × 10^-22 m

The De Broglie wavelength of proton with 500 eV kinetic energy is:

λ = 1.657 × 10^-12 m