Structure of Atom — Practice

Question 1

Find the wavelength of the H-alpha line (n=3 to n=2) in the Balmer series. (R_H = 1.097 x 10^7 m^-1)

Accepted Answer

1/lambda = R_H(1/4 - 1/9) = 1.097x10^7 x 5/36 = 1.524x10^6 m^-1. lambda = 656.3 nm.

Question 2

Find the de Broglie wavelength of an electron moving at 2 x 10^6 m/s (m = 9.1 x 10^-31 kg).

Accepted Answer

lambda = h/mv = 6.626x10^-34 / (9.1x10^-31 x 2x10^6) = 3.64 x 10^-10 m = 3.64 Angstrom.

Question 3

Write the four quantum numbers for the 3p electron of aluminium (Z=13).

Accepted Answer

Al: 1s2 2s2 2p6 3s2 3p1. For the 3p electron: n=3, l=1, m_l = +1 (any of -1, 0, +1), m_s = +1/2.

Question 4

Calculate the uncertainty in position if the uncertainty in velocity is 0.001 m/s for an electron (m = 9.1 x 10^-31 kg).

Accepted Answer

delta-p = m x delta-v = 9.1x10^-34. delta-x >= h/(4 pi delta-p) = 6.626x10^-34 / (4 x 3.14 x 9.1x10^-34) = 0.058 m.

Question 5

Why is chromium's configuration [Ar]4s1 3d5 instead of [Ar]4s2 3d4?

Accepted Answer

A half-filled 3d5 subshell has extra stability due to symmetrical distribution and exchange energy, so one 4s electron shifts to 3d to achieve the more stable half-filled configuration.

Practice — Structure of Atom

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