Which statements are true for an electron in the 1s orbital of hydrogen ? 1. The...

Which statements are true for an electron in the 1s orbital of hydrogen ?

1. The potential energy of the electron is negative.

2. The total energy of the electron is constant.

3. The kinetic energy of the electron is positive.

Solutions

Expert Solution

1.The hydrogen atom represents the simplest possible atom, since it consists of only one proton and one electron. The electron is bound, or confined. Its potential energy function U(r) expresses its electrostatic potential energy as a function of its distance r from the proton.

U(r) = -q²/(4πε₀r) = -e²/r..Here e² is defined as q²/(4πε₀). In SI unit 1/(4πε₀) = 9*10⁹ Nm²/C², and q = 1.6*10^-19 C.

The figure on the right shows the shape of U(r) in a plane containing the origin. The potential energy is chosen to be zero at infinity. The electron in the hydrogen atom is confined in the potential well, and its total energy is negative. TRue

E_n = -me⁴/(2ħ²n²) = -13.6 eV/n².

Here n is called the principle quantum number. The values E_n are the possible value for the total electron in the hydrogen atom..

3.The average potential energy is -me⁴/(ħ²n²) and the average kinetic energy is me⁴/(2ħ²n²).True

queen_honey_blossom answered 1 year ago

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