Physics

Electromagnetic Waves and Spectrum

659 Questions

Electromagnetic waves and spectrum questions test a candidate's understanding of radiation frequencies, wavelengths, and the properties of different rays like infrared, ultraviolet, and visible light. Concepts also cover practical applications in astronomy and the fundamental speed of light calculations. This physics topic appears regularly in general science sections of major competitive examinations.

UV rays propertiesElectromagnetic radiation frequencyWavelength identificationSpeed of light calculationsBlack body radiation

Electromagnetic Waves and Spectrum Questions

Multiple choice kirchoff's laws black body radiation heat transfer thermal properties physics

The maximum wavelength of radiations emitted at 900 K is $4 \mu m$. What will be the maximum wavelength of radiation emitted at 1200 K?

  1. 3 $\mu m$
  2. 0.3 $\mu m$
  3. 1 $\mu m$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to Wien's displacement law, the product of maximum wavelength and absolute temperature is constant, so lambda_1 * T1 = lambda_2 * T2. Substituting the given values, 4 micrometers * 900 K = lambda_2 * 1200 K, which gives lambda_2 = (4 * 900) / 1200 = 3 micrometers.

Multiple choice kirchoff's laws black body radiation heat transfer thermal properties physics

Certain substance emit only the wavelength $\lambda  _{1},\lambda  _{2},\lambda  _{3}  \ and  \ \lambda  _{4}$ when it is at a high temperature. When this substance is at a colder temperature, it will absorb only the following wavelength :

  1. $\lambda _{1}$
  2. $\lambda _{2}$
  3. $\lambda _{1}$ and $\lambda _{2} $
  4. $\lambda _{1},\lambda _{2},\lambda _{3}$ and $\lambda _{4} $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

With the help of kirchhoff's law  we can say that $\varepsilon =\alpha $
${\varepsilon}= emissivity $
$\alpha=absorptivity $
so kirchhoff's law state that total emissivity of body is equal to total absorptivity.
so ${\lambda} _{1},{\lambda} _{2}, {\lambda} _{3}, {\lambda} _{4}$ will be absorbed.  

Multiple choice kirchoff's laws black body radiation heat transfer thermal properties physics

In a dark room with ambient temperature $T _o$, a black body is kept at a temperature $T$. Keeping the temperature of the black body constant (at $T$), sunrays are allowed to fall on the black body through a hole in the roof of the dark room. Assuming that there is no change in the ambient temperature of the room, which of the following statement(s) is/are correct?

  1. The quantity of radiation absorbed by the black body in unit time will increase

  2. Since emissivity = absorptivity, hence the quantity of radiation emitted by black body in unit time will

    increase

  3. Black body radiates more energy in unit time in the visible spectrum.

  4. The reflected energy in unit time by the black body remains same.
Reveal answer Fill a bubble to check yourself
A,B,C,D Correct answer
Explanation

Since the radiation is continuously falling on the black body, the quantity radiation absorbed per second will increase.

The reason given in question is self explanatory.
With an increase in temperature, the entire Plank's curve shifts upwards and hence radiation in any spectrum will increase.
Reflected energy per unit time will be zero since black body has 0 reflectivity and hence it will remain constant.  

Multiple choice standardized measurement measurement of physical quantities need of unit for measurement measurements and experimentation physics

The wavelength of light is usually expressed in

  1. Micron

  2. Fermi

  3. Nanometer

  4. Angstrom
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Angstrom $(\dot A)$ unit of length used chiefly in measuring wavelengths of light, equal to $10^{-10}$ metre, or $0.1$ nanometer.  It is used to express wavelengths of visible light, ultraviolet (UV) light, X rays, and gamma rays.

Multiple choice standardized measurement measurement of physical quantities need of unit for measurement measurements and experimentation physics

The wavelength of light is expressed in

  1. Metre

  2. Micron

  3. Light year

  4. Angstrom
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Angstrom $(\dot A)$ unit of length used chiefly in measuring wavelengths of light, equal to $10^{-10}$ metre, or $0.1$ nanometer.  It is used to express wavelengths of visible light, ultraviolet (UV) light, X rays, and gamma rays.

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

Choose the correct answer from the alternatives given.
A plane electromagnetic wave of frequency $25 MHz$ travels in free space along $X$-direction. At a particular point in space and time, electric field $\vec E=6.3\ \hat j\ V/m$. What is $B$ at this point.

  1. $1.2 \, \times \, 10^{-6} \, T$
  2. $1.2 \, \times \, 10^{-8} \, T$
  3. $2.1 \, \times \, 10^{-6} \, T$
  4. $2.1 \, \times \, 10^{-8} \, T$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given: The frequency of the electromagnetic wave is $25\ MHz$.

The electric field at the particular point is $6.3\hat j\ V/m$

To find: The magnetic field at that point.

The magnetic field of the electromagnetic wave at a point is given by:
$B = \dfrac{E}{c}\= \dfrac{6.3}{3 \times 10^8}\ \Rightarrow2.1 \times 10^{-8} T$

So, option $(D)$ is correct.

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

The electric field of an electromagnetic wave traveling through the vacuum is given by the equation $E=E _0\ sin (Kx-\omega t).$ The quantity that is independent of wavelength is:

  1. $k\omega$
  2. $\dfrac{k}{\omega}$
  3. $k^2\omega$
  4. $\omega$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find: The quantity that is independent of the wavelength.


The angular frequency $\omega$ is given by:
$\omega \, = \, 2\pi \nu$
The frequency of a wave varies with the wavelength. So, angular frequency is dependent on wavelength.

The quantity $k$ is defined as the wavenumber and it is given by:
$k = \dfrac{2\pi}{\lambda}$
It shows that $k$ is dependent on wavelength.


The value of $\dfrac{k}{\omega}$ can be obtained as:
$\dfrac {k}{\omega} \, = \, \dfrac{2\pi / \lambda}{2\pi \nu}\\implies \, \dfrac{1}{\nu \lambda} \, = \, \dfrac{1}{c}\,\,\ \ \ \ \ \ \ \ \ \ \ \ \  (\because \, c \, = \, \nu \lambda)$
where c is the speed of electromagnetic wave in vacuum. It is a constant whose value is $3 \, \times \, 10^8 \, ms^{-1}$.

So, option $(B)$ is correct.

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

According to Maxwell's equation, the velocity of light in any medium is expressed as

  1. $\displaystyle\frac{1}{\sqrt{\mu _0\varepsilon _o}}$
  2. $\displaystyle\frac{1}{\sqrt{\mu\varepsilon}}$
  3. $\displaystyle\sqrt{\frac{\mu}{\varepsilon}}$
  4. $\displaystyle\sqrt{\frac{\mu _0}{\varepsilon}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Velocity of light in a medium,

$\displaystyle c=\frac{1}{\sqrt{\mu _0\varepsilon _o\mu _r\varepsilon _r}}=\frac{1}{\sqrt{\mu\varepsilon}}$

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

The electric field associated with an e.m. wave in vacuum is given by $\vec {E} = 40\cos (kz - 6\times 10^{8}t)\hat {i}$, where $E, z$ and $t$ in $volt/m$, meter and seconds respectively. The value of wave vector $k$ is

  1. $6m^{-1}$
  2. $3m^{-1}$
  3. $2m^{-1}$
  4. $0.5m^{-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given: The electric field associated with  an electromagnetic wave in vacuum is given by $\vec E =40 \cos(kz−6\times 10^8t)\hat i$  , where E, z and t are in volt per meter, meter and second respectively.
To find the value of wave vector k
Solution: 
We know electromagnetic wave eqution is
$E=E _0\cos(kz-\omega t)$
And given equation is
$\vec E =40 \cos(kz−6\times 10^8t)\hat i$
By comparing these two, we get
$\omega=6\times10^8$ and 
$E _0=40\hat i$
we also know,
Speed of electromagnetic wave, $v=\dfrac \omega k$
where v is the speed of the light
Hence, $k=\dfrac \omega v\\\implies k=\dfrac {6\times 10^8}{3\times 10^8}\\\implies k=2m^{-1}$
is the required value
Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

Wavelength of light in different media are proportional to:

  1. speed of light in that medium

  2. Amplitude of light in that medium

  3. frequency of light in that mrdium

  4. Nove of above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The speed of light in a medium is given by v = f * lambda. Since frequency (f) remains constant when light moves between media, the wavelength (lambda) is directly proportional to the speed of light (v) in that medium.

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

A plane electromagnetic wave with an intensity of $200 W/m^2$ is incident normal to a flat plate of radius 30 cm. If the plate absorbs $60%$ and reflect $40%$ of the incident radiation, what is the momentum transferred to it in 5 min?

  1. $1.7 \times 10^{-3} kg ms^{-1}$
  2. $2.7 \times 10^{-4} kg ms^{-1}$
  3. $3.7 \times 10^{-4} kg ms^{-1}$
  4. $3.7 \times 10^{-3} kg ms^{-1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice chemistry introduction to analytical chemistry interpreting a balanced chemical reaction percentage yield stoichiometric calculations

One mole of photons is known as one Einstein of radiation. According to Stark-Einstein law of photochemical equivalence, one mole of reactant absorbs one Einstien of energy. For a photochemical reaction, a term called quantum yield is defined as:
Quantum yield $ (\phi) = \dfrac {No. \,of \,moles \,of \,reactant \,converted} {No. \,of \,Einstein \,absorbed} $
The correct statement(s) is/are:

  1. for a chain reaction $\phi _{gas} >> \phi _{solution}$
  2. in a photochemical chain reaction $\phi >> 1$
  3. in a photochemical chain reaction $\phi << 1$
  4. for a chain reaction $\phi _{gas} << \phi _{solution}$
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation
$Quantum \ Yield= \cfrac {Number \ of \ moles \ of \ reactant \ converted}{Number \ of \ einstein \ absorbed}$
An einstein of radiation $=$ one mole of photons
For a chain reaction, $\phi _{gas} >> \phi _{solution}$
and ln photochemical chain reaction $\phi >>1$