Question

31) For the Bohr hydrogen atom determine: (½ pt each = 2 pts total)

(a) The radius of the orbit n = 4:

(b) Whether there is an orbit having a radius of 4.00 Angstroms: *please be detailed

(c) The energy level corresponding to n = 8:

(d) Whether there is an energy level at– 2.5 x 10^17 J:

Answer 1

(a) The radius of the n^th orbit for the Bohr's hydrogen atom = r1*n²

Here, r1 = radius of 1st Bohr orbit of hydrogen atom = 0.529 A^o

Therefore, r4 = 4²*0.529 A^o = 8.464 A^o

(b) No, there is no orbit with a radius of 4 A^o.

Explanation: 4 A^o/0.529 A^o = 7.56

Here, 7.56 is not a perfect square. Hence, there is no orbit having a radius of 4 A^o

(c) The energy of the n^th orbit for the Bohr's hydrogen atom = E1/n²

Here, E1 = energy of 1st Bohr orbit of hydrogen atom = -328 kJ/mol

Therefore, E8 = -328/8² kJ/mol = -5.125 kJ/mol

(d) No, there is no energy level at -2.5*10¹⁷ J

Explanation: -328 J/-2.5*10¹⁷ J = 131.2*10^-17

Here,131.2*10^-17 is not a perfect square. Hence, there is no energy level at -2.5*10¹⁷ J.