In the Bohr model of hydrogen, the circumference of an orbit equals nlambda and r_n = n^2 a_0 with a_0 = 0.529 AA. Find the de Broglie wavelength of the electron in the n=3 orbit in AA, to two decimals (use pi=3.1416).

JEE Advanced levelNumerical answerDifficulty 3 of 3as149

In the Bohr model of hydrogen, the circumference of an orbit equals $nλ$ and $r_{n} = n^{2} a_{0}$ with $a_{0} = 0.529 \overset{˚}{A}$ . Find the de Broglie wavelength of the electron in the $n = 3$ orbit in $\overset{˚}{A}$ , to two decimals (use $π = 3.1416$ ).

Numerical answer type, answer in Angstrom, tolerance 0.02.

r_{3} = 9 \times 0.529 = 4.761 \overset{˚}{A}

λ = 2 π r_{3} /3 = 9.971 \overset{˚}{A}