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Standard XII

Chemistry

Bohr's Model of a Hydrogen Atom

The Bohr mode...

Question

The Bohr model of the atom was able to explain the Balmer series because :

larger orbits required electrons to have more negative energy in order to match the angular momentum.

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differences between the energy levels of the orbits matched the difference between energy levels of the line spectra.

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electrons were allowed to exist only in allowed orbits and nowhere else.

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none of the above.

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Solution

The correct option is B differences between the energy levels of the orbits matched the difference between energy levels of the line spectra.
The Bohr model of the atom was able to explain the Balmer series because differences between the energy levels of the orbits matched the difference between energy levels of the line spectra.

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Q. The only electron in the hydrogen atom resides under ordinary conditions on the first orbit. When energy is supplied, the electron moves to higher energy orbit depending on the amount of energy absorbed. When this electron returns to any of the lower orbits, it emits energy. Lyman series is formed when the electron returns the lowest orbit while Balmer series is formed when the electron returns to the second orbit. Similarly, Paschen, Brackett, and Pfind series are formed when electron returns to the third, fourth, and fifth from higher orbits, respectively.
Maximum number of lines produced when an electron jumps from nth level to ground level is equal to

\frac{n (n - 1)}{2}

.
If the electron comes back from the energy level having energy E

_{2}

to the energy level having energy E

_{1}

, then difference may be expressed in terms of energy of photon as
E

_{2}

- E

_{1}

Δ

λ

= hc/

Δ

E
Since h and c are constant,

Δ

E corresponds to definite energy, thus, each transition from one energy level to another will produce a light of definite wavelength. This is actually observed as a line in the spectrum of hydrogen atom.
Wave number of line is given by the formula
v =

R Z^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})

where R is a Rydberg constant.The wave number of electromagnetic radiation emitted during the transition of electron in between the two levels of Li

^{2 +}

ion whose principal quantum numbers sum is 4 and difference is 2 is :

Q. (a) Using Bohr's postulates, obtain the expression for total energy of the electron in the

n^{t h}

orbit of hydrogen atom.
(b) What is the significance of negative sign in the expression for the energy?
(c) Draw the energy level diagram showing how the line spectra corresponding to Paschen series occur due to transition between energy levels.

The only electron in the hydrogen atom resides under ordinary conditions on the first orbit. When energy is supplied, the electron moves to higher energy orbit depending on the amount of energy absorbed. When this electron returns to any of the lower orbits, it emits energy. Lyman series is formed when the electron returns to the lowest orbit while Balmer series is formed when the electron returns to second orbit. Similarly, Paschen, Brackett and Pfund series are formed when electron returns to the third, fourth and fifth orbits from higher energy orbits respectively. The maximum number of lines produced when an electron jumps from nth level to ground level is equal Maximum number of lines produced when an electron jumps from nth level to ground level is equal to.

\frac{1 (n - 1)}{2} .

For example, in the case of

n = 4,

number of lines produces is 6.

(4 \to 3, 4 \to 2, 4 \to 1, 3 \to 2, 3 \to 1, 2 \to 1) .

When an electron returns from to state, the number of lines in the spectrum will be equal to

\frac{(n_{2} - n_{1}) (n_{2} - n_{1} + 1)}{2}

If the electron comes back from energy level having energy to energy level having energy, then the difference may be expressed in the terms of energy of photon as

E_{2} - E_{1} Δ E, λ = \frac{h c}{Δ E}

Since h and c are constants,

Δ E

corresponds to definite energy; thus each transition from one energy level to another will produce a light of definite wavelength. This is observed as a line in the spectrum of the hydrogen atom. Wavenumber of line is given by the formula

¯ v = (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) .

where R is a Rydberg's constant

(R = 1.1 \times 10^{7} m^{- 1})

The energy photon emitted corresponding to transition n = 3 to n=1 is:

[

h = 6 \times 10^{- 34} J - s e c]

Q. When energy is supplied to an atom, the electrons of the atom move to higher energy orbits depending on the amount of energy absorbed. When these electrons return to any of the lower energy orbits, they emit energy. Depending on whether the electrons return to the 1st, 2nd, 3rd, 4th or 5th orbits, the series formed are called Lyman, Balmer, Paschen, Brackett and Pfund series respectively.
If the electron comes back from the energy level

E_{2}

to the energy level

E_{1}

, then the difference may be expressed in terms of the energy of photon as

E_{2} - E_{1} = Δ E

λ = \frac{h c}{Δ E}

Thus each transition from one energy level to another will produce a light of definite wavelength. This is observed as a line in the spectrum of the hydrogen atom.
Wave number of the line is given by the formula

- ν = R Z^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})

Where

R = 1.097 \times 10^{5} c m^{- 1}

is Rydberg constant.

\begin{matrix} List - I & List - II (I) If the ionisation potential for hydrogen-like atom & (P) 5.48 \times 10^{- 32} c R J in a sample is 122.0 e V, then the energy of the last line of Paschen series for this atom is: (II) In a single isolated atom, an electron makes & (Q) 6.6 \times 10^{- 32} c R J transition from fifth excited state such that no spectral lines are observed in the visible range then maximum number of different types of photons observed is: (III) The difference in energy of the second line & (R) 6 of Lyman series and last line of Brackett series in a hydrogen sample is: (IV) The energy of the electromagnetic radiation & (S) 4 emitted during the transition of electron in between the two levels of L i^{2 +} ion whose principal quantum number sum is 4 and difference is 2 is: (T) 6.6 \times 10^{- 34} c R J (U) 0.53 \times 10^{- 30} c R J \end{matrix}

Which of the following options has the correct combination considering List-I and List-II?

Q. The ratio of the difference in energy of electron between the first and second Bohrs orbit to that between second and third Bohrs orbit is:

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