Hydrogen atoms absorb energy so that the electrons are excited to the energy lev

Question

Hydrogen atoms absorb energy so that the electrons are excited to the energy level n = 7. Electrons then undergo these transitions: (1) n = 7 rightarrow n = 1; (2) n = 7 rightarrow n; (3) n = 2 rightarrow n. Which of these transitions will produce the photon with (a) the smallest energy; (b) the highest frequency; (c) the shortest wavelength? (d) What is the frequency of a photon resulting from the transition n = 6 rightarrow n = 1? Write the subshell notations that correspond to: a. n = 3, l = 2 _____ b. n = 1, l = 0 _____ c. n = 4, l = 3 _____ d. l = 3, M_l _____ In the following table, indicate the values of the four quantum numbers for the electrons: n l M_l M_s

Explanation / Answer

1. (a)

Energy of an electron for an energy level n in hydorgen atom is given by,

En = -13.6eV/n2

For transition n = 7 to n = 1, the energy of the photon emitted is

E71 = -13.6eV/72- (-13.6eV/12) = -13.6eV/72 +13.6eV/12 = 13.32eV

For transition n = 7 to n = 2, the energy of the photon emitted is,

E72 = -13.6eV/72- (-13.6eV/22) = -13.6eV/72 +13.6eV/22 = 3.12eV

For transition n = 2 to n = 1, the energy of the photon emitted is,

E21 = -13.6eV/22- (-13.6eV/12) = -13.6eV/22 +13.6eV/12 = 10.2eV

So, the smallest energy photon will be released for transition from n = 7 to n = 2

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1.(b)

A seen above, the highest energy photon will be released for transition from n = 7 to n = 1.

And, Energy = hf, where f is the frequency, so energy is directely propotional to frequency.

So transition from n = 7 to n = 1 will also have the highest frequency.

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1.(c)

The highest energy photon will be released for transition from n = 7 to n = 1 with highest frequency. Frequency is inversely proportional to wavelength, so,

transition from n = 7 to n = 1 will have shortest wavelength.

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1.(d)

For transition n = 6 to n = 1, the energy of the photon emitted is

E61 = -13.6eV/62- (-13.6eV/12) = -13.6eV/62 +13.6eV/12 = 13.22eV

Let the frequency be f, then

hf = 13.22eV

or f = (13.22eV)/(4.1357 × 10-15 eV s)

or f = 3.19X1015 Hz

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This concludes the answers. Check the answer and let me know if it's correct. If you need any more clarification or correction, feel free to ask.....

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