Anonymous
Anonymous asked in Science & MathematicsPhysics · 4 months ago

# What is the speed of an electron with kinetic energy 780 eV? What is the speed of an electron with kinetic energy 0.40 keV?

A) What is the speed of an electron with kinetic energy 780 eV?

B) What is the speed of an electron with kinetic energy 0.40 keV?

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• Anonymous
4 months ago

1 ev = 1.60*10^-19 joule

A)

E = 780 ev = 1.25*10^-16 joule

mass of el. m = 9.11*10^-31 kg

speed V = √2E/m = √25*10^-17*10*31/9.11 = 10^7√25/9.11 = 1.66*10^7 m/sec

B)

E = 400 ev = 0.64*10^-16 joule

mass of el. m = 9.11*10^-31 kg

speed V = √2E/m = √12.8*10^-17*10*31/9.11 = 10^7√25/9.11 = 1.18*10^7 m/sec

• 4 months ago

780 eV = 1.25e-16 J

mass of electron is 9.1e-31 kg

KE = ½mV² = 1.25e-16 J

V = √(2•1.25e-16/9.1e-31) = 1.66e7 m/s

which is close to the speed of light, so you should use the equation below, which gets complicated.

mc²(γ–1) = 1.25e-16

γ–1 = 1.25e-16 / (9.1e-31)(3e8)² = 0.0015284

γ = 1/√(1–(V²/c²)) = 1.0015284

√(1–(V²/c²)) = 0.998474

1–(V²/c²) = 0.9969503

V²/c² = 0.0030497

V/c = 0.0552244

V = 1.656e7 m/s

so the error is small

second one is similar, but slower, so the first equations are fine

Relativistic KE = mc²γ–mc² = mc²(γ–1)

γ = 1/√(1–(V²/c²))

Kinetic Energy in J if m is in kg and V is in m/s

KE = ½mV²