The energies $E_1$ and $E_2$ of two radiations are 25 eV and 50 eV respectively. The relation between their wavelengths i.e. $\lambda_1$ and $\lambda_2$ will be (a) $\dfrac{\lambda_1}{\lambda_2}=1$ (b) $\lambda_1=2\lambda_2$ (c) $\lambda_1=\sqrt{25\times50}\,\lambda_2$ (d) $2\lambda_1=\lambda_2$

The energies E₁ and E₂ of two radiations are 25 eV and 50 eV respectively. The relation between their waveleng

Choose the Best Answer · Q3

E_1

(a)

\dfrac{\lambda_1}{\lambda_2}=1

(b)

\lambda_1=2\lambda_2

(c)

\lambda_1=\sqrt{25\times50}\,\lambda_2

(d)

2\lambda_1=\lambda_2

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✓ Free question

Concept understanding — Bohr's Atom Model

Niels Bohr rescued Rutherford's nuclear atom from classical electromagnetism's prediction of collapse by proposing that electrons occupy only certain fixed, non-radiating stationary orbits, in which the angular momentum is quantised as an integer multiple of $h/2\pi$ : $mvr=nh/2\pi$ . While an electron sits in a stationary orbit it does not radiate energy, no matter what classical theory says about accelerated charges - this single postulate is what makes atoms stable. An electron only emits or absorbs energy when it jumps between orbits, and the photon involved carries exactly the energy difference between the two orbits, $E_2-E_1=h\nu$ .

For any one-electron ("hydrogen-like") species of atomic number $Z$ - hydrogen itself, or an ion such as $\text{He}^+$ or $\text{Li}^{2+}$ - solving the model gives closed-form results for the radius and energy of the $n$ th orbit:

r_n=\left(0.529\,\frac{n^2}{Z}\right)\text{Å}\qquad\qquad E_n=-\left(\frac{13.6\,Z^2}{n^2}\right)\text{eV atom}^{-1}=-\left(\frac{1312.8\,Z^2}{n^2}\right)\text{kJ mol}^{-1}

The negative sign reflects that a bound electron is at lower energy than a free electron at infinite separation (taken as zero). Because energy depends on $1/n^2$ , energy gaps between successive levels shrink rapidly as $n$ grows - so transitions between high, closely-spaced levels release far less energetic photons than transitions down to the ground state. Since $E_n\propto Z^2$ , one-electron ions of different $Z$ (like $\text{H}$ and $\text{He}^+$ ) have spectra of an identical mathematical shape, just scaled by $Z^2$ - hydrogen-like species with the same electron count really do behave like scaled copies of each other.

Despite its success with hydrogen, the model applies only to one-electron species, cannot account for spectral-line splitting in magnetic or electric fields (the Zeeman and Stark effects), and offers no physical reason for its own central assumption of quantised angular momentum - a gap only closed once de Broglie's wave picture of the electron was developed.

Step 1. From $E=hc/\lambda$ , wavelength and energy are inversely proportional: $\lambda\propto1/E$ .

Step 2. So $\dfrac{\lambda_1}{\lambda_2}=\dfrac{E_2}{E_1}=\dfrac{50}{25}=2$ , i.e. $\lambda_1=2\lambda_2$ .

Step 3. This matches option (b). Option (a) would require $E_1=E_2$ , which is not given; option (c) proposes $\lambda_1=\sqrt{25\times50}\,\lambda_2$ , an arbitrary combination with no basis in $E=hc/\lambda$ ; option (d) inverts the correct ratio.

✓Final answer

\lambda_1=2\lambda_2

Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2022Set ANNUAL1 markMCQ
$Q. Splitting of spectral lines in an electric field is called:$
(a) Compton effect
(b) Zeeman effect
(c) Stark effect
(d) Shielding effect
›Reveal solutionSolution
Splitting of spectral lines in an electric field is the Stark effect; splitting in a magnetic field (a different phenomenon) is the Zeeman effect.

When atoms that would normally emit a single spectral line are placed in an external field, that line can split into several closely spaced lines because the field removes some of the degeneracy of the atomic energy levels:

In a magnetic field, this splitting is called the Zeeman effect.

In an electric field, this splitting is called the Stark effect.

The Compton effect refers to a completely different phenomenon — the increase in wavelength of X-rays scattered by electrons.

'Shielding effect' refers to inner electrons reducing the effective nuclear charge felt by outer electrons, unrelated to spectral line splitting.

Since the question specifies an electric field, the correct term is the Stark effect.

✓Final answer
$The answer is (c) Stark effect — spectral line splitting caused specifically by an electric field.$
CBSE 2019Set ANNUAL1 markMCQ
$Q. Splitting of spectral lines in an electric field is called:$
(a) Compton effect
(b) Stark effect
(c) Zeeman effect
(d) Shielding effect
›Reveal solutionSolution

Splitting of spectral lines under an applied electric field is called the Stark effect.

When atoms that are emitting or absorbing radiation are placed in a strong external electric field, their spectral lines split into several closely spaced components. This is the Stark effect, discovered by Johannes Stark, and it arises because the electric field perturbs (shifts) the energy levels of the atom depending on their orientation relative to the field.

This should not be confused with the Zeeman effect (option c), which is the analogous splitting of spectral lines produced by an external magnetic field rather than an electric field. The Compton effect (option a) refers to the change in wavelength of X-rays on scattering from electrons, and "shielding effect" (option d) refers to inner electrons reducing the effective nuclear charge felt by outer electrons — neither involves splitting of spectral lines.

✓Final answer
$The correct option is (b) Stark effect.$
CBSE 2018Set ANNUAL1 markMCQ
$Q. Consider the following statements. (I) The number of electrons in an atom is equal to the number of neutrons in it. (II) The number of protons in an atom is called its mass number. (III) Electrons and the nucleus are held together by electrostatic forces of attraction. Which of the above statement/s is/are not correct?$
(a) (I) and (III)
(b) (I) and (II)
(c) (I), (II) and (III)
(d) (II) and (III)
›Reveal solutionSolution

Statements (I) and (II) are factually incorrect; only statement (III) is correct.

Examine each statement:

(I) 'The number of electrons in an atom is equal to the number of neutrons in it' - this is FALSE. In a neutral atom, the number of electrons equals the number of PROTONS (the atomic number Z), not the number of neutrons. Electrons equal neutrons only coincidentally for a few specific atoms, not as a general rule.

(II) 'The number of protons in an atom is called its mass number' - this is FALSE. The number of protons is called the atomic number (Z). The mass number (A) is the sum of the number of protons AND neutrons (A = Z + N).

(III) 'Electrons and the nucleus are held together by electrostatic forces of attraction' - this is TRUE. The positively charged nucleus (protons) attracts the negatively charged electrons via Coulombic (electrostatic) force, which is what keeps electrons bound within the atom.

So the statements that are NOT correct are (I) and (II).

✓Final answer
$The correct option is (b): statements (I) and (II) are not correct.$

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Q.The energies $E_1$ and $E_2$ of two radiations are 25 eV and 50 eV respectively. The relation between their wavelengths i.e. $\lambda_1$ and $\lambda_2$ will be

Unlock everything free for 14 days