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Bohr's Model of a Hydrogen Atom

When electron...

Question

When electronic transition occurs from higher energy state to a lower energy state with energy difference equal to $Δ E$ expressed in electron volts, the wavelength of line emitted is approximately equal to:

A

\frac{12375}{Δ E} A^{o}

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B

\frac{12375}{Δ E} \times 10^{- 8} c m

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C

\frac{12375}{Δ E} \times 10^{- 10} m

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D

either of these

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Solution

The correct option is C either of these
As we know,
$E = h v = h c / λ$
$δ E = E_{2} - E_{1} = h c / λ$
$Δ E (e V) = \frac{12375}{λ}$ ;
where $λ$ in $A^{o}$ .

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Q. The frequency of radiation absorbed or emitted when transition occurs between two stationary states that differ in energy by:

Δ E

v = \frac{Δ E}{h} = \frac{E_{2} - E_{1}}{h}

E_{1}

E_{2}

are the energies of the lower and higher allowed energy states respectively. This expression is?

Q. During the transition of an electron from higher state to lower state, a photon is emitted having energy equal to

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 Pfund series are formed when an electron returns to the third, fourth, and fifth from higher orbits, respectively.
A 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 E

λ = \frac{h c}{Δ E}

h

c

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 a 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}})

R

is a Rydberg constant.

In a single isolated atom, an electron makes transition from a fifth excited state to second state then maximum number of different types of photons observed is :

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]

During the emission spectrum of electron in $H e^{+}$ ion, the electron on transition from same higher energy state drops to the ground state and first excited state emits two photon of $λ_{1}$ =304 $A^{\circ}$ and $λ_{2}$ =1085 $A^{\circ}$ respectively.The total number of photons emitted during the transition of electrons from highest excited to all lower energy level(Possible)

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