An electron is in an excited state in a hydrogen-like atom. It has a t

1.	An electron is in an excited state in a hydrogen-like atom. It has a total energy of -3.4 eV. The kinetic energy of the electron is E and its de Broglie wavelength is λ.(a) E = 6.8 eV, λ ~ 6.6 x 10-10 m(b) E = 3.4 eV, λ ~ 6.6 x 10-10 m (c) E = 3.4 eV, λ ~ 6.6 x 10-11 m (d) E = 6.8 eV, λ ~ 6.6 x 10-11 m
Answer» Correct Answer is: (b) E = 3.4 eV, λ ~ 6.6 x 10^-10 m The potential energy = -2 x kinetic energy = -2E. ∴ total energy = -2E + E = -E = -3.4 eV or E = 3.4 eV. Let p = momentum and m = mass of the electron. ∴ E = p²/2m or p = √(2mE). de Broglie wavelength , λ = h/p = h/√(2mE) ~ 6.6 x 10^-10 m.

An electron is in an excited state in a hydrogen-like atom. It has a total energy of -3.4 eV. The kinetic energy of the electron is E and its de Broglie wavelength is λ.(a) E = 6.8 eV, λ ~ 6.6 x 10-10 m(b) E = 3.4 eV, λ ~ 6.6 x 10-10 m (c) E = 3.4 eV, λ ~ 6.6 x 10-11 m (d) E = 6.8 eV, λ ~ 6.6 x 10-11 m

Answer»

Correct Answer is: (b) E = 3.4 eV, λ ~ 6.6 x 10^-10 m

The potential energy = -2 x kinetic energy = -2E.

∴ total energy = -2E + E = -E = -3.4 eV

or E = 3.4 eV.

Let p = momentum and m = mass of the electron.

∴ E = p²/2m

or p = √(2mE).

de Broglie wavelength , λ = h/p = h/√(2mE) ~ 6.6 x 10^-10 m.

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