Question

Verify the ground state energy (E₀) as 13.6 eV using (E₀ = {{2π²q⁴e²}}/{{mek²h²}}).

a) (13.6 , {eV})
b) (3.14 , {eV})
c) (6.022 , {eV})
d) (9.81 , {eV})

Answer 1

The ground state energy of hydrogen is verified using a formula involving physical constants, yielding an experimentally verified value of -13.6 eV. This represents the energy needed to ionize a hydrogen atom from its ground state. The correct option is A.

Step-by-step explanation:

To verify that the ground state energy (E0) of hydrogen is 13.6 eV, we can use the given formula E0 = (2π²q4e²)/(mek²h²), where 'q' is the elementary charge, 'e' is the electron charge, 'me' is the electron mass, 'k' is Coulomb's constant, and 'h' is Planck's constant.

Plugging in these constants (with their respective units) into the formula and simplifying, we should obtain an energy value close to -13.6 eV. This energy corresponds to the energy needed to ionize hydrogen from its ground state, which is an experimentally verified number. The negative sign indicates that this is a bound state, and the electron would need this amount of energy to be freed from the nucleus.