derive an expression for energy electron in the nth Bohr orbit calculate the wavelength of first line in paschen series of hydrogen atom
Answers
Energy of the electron in `nth` orbit of hydrogen atom is given by `E_(n) =-(13.6)/(n^(2))eV`. Bohr's model of the hydrogen atom is based on three postulates: (1) an electron moves around the nucleus in a circular orbit, (2) an electron's angular momentum in the orbit is quantized, and (3) the change in an electron's energy as it makes a quantum jump from one orbit to another is always accompanied. We know that energy of nth orbit, En = -K/n2 (for hydrogen atom), where K is a constant. So we have to know the value of 'K'. By keeping the electrons in circular, quantized orbits around the positively-charged nucleus, Bohr was able to calculate the energy of an electron in the nth energy level of hydrogen: E ( n ) = − 1 n 2 ⋅ 13.6 eV E(n)=-\dfrac{1}{n^2} \cdot 13.6\,\text{eV} E(n)=−n21⋅13.