Question
When the electron orbiting in hydrogen atom in its ground state moves to the third excited state, show how the de Broglie wavelength associated with it would be affected.
✓
Answer
de Broglie wavelength $\lambda = \frac{\text{h}}{\text{mv}}$
$\therefore \lambda \propto\frac{1}{v} ; \text{v} \propto\frac{1}{\text{n}}$
$\therefore \lambda\propto\text{n}$
$\therefore$ ?? Broglie wavelength will increase
Alternate Answer
As $2\pi\text{r}_{n} = \text{n}\lambda ; \lambda = \frac{2\pi\text{r}_{n}}{\text{n}}(\lambda\propto\frac{\text{r}_{n}}{\text{n}})$
$\text{r}_{n}\propto\text{n}^{2}$
$\therefore \lambda\propto\frac{\text{n}^{2}}{\text{n}}\Rightarrow\lambda\propto\text{n}$
$\therefore$ ?? Broglie wavelength will increase.
$\therefore \lambda \propto\frac{1}{v} ; \text{v} \propto\frac{1}{\text{n}}$
$\therefore \lambda\propto\text{n}$
$\therefore$ ?? Broglie wavelength will increase
Alternate Answer
As $2\pi\text{r}_{n} = \text{n}\lambda ; \lambda = \frac{2\pi\text{r}_{n}}{\text{n}}(\lambda\propto\frac{\text{r}_{n}}{\text{n}})$
$\text{r}_{n}\propto\text{n}^{2}$
$\therefore \lambda\propto\frac{\text{n}^{2}}{\text{n}}\Rightarrow\lambda\propto\text{n}$
$\therefore$ ?? Broglie wavelength will increase.
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Radio waves are produced by the accelerated motion of charges in conducting wires. Microwaves are produced by special vacuum tubes. Infrared waves are produced by hot bodies and molecules also known as heat waves. UV rays are produced by special lamps and very hot bodies like Sun.
(i) Solar radiation is
i. transverse electromagnetic wave
ii. longitudinal electromagnetic waves
iii. both longitudinal and transverse electromagnetic waves
iv. none of these.
(a) Option (i) (b) Option (iv) (c) Option (iii) (d) Option (ii)
(ii) What is the cause of greenhouse effect?
(a) Ultraviolet rays (b) X-rays (c) Infrared rays (d) Radiowaves
(iii) Biological importance of ozone layer is
(a) it stops ultraviolet rays
(b) none of these.
(c) it reflects radiowaves
(d) It layer reduces greenhouse effect
OR
Earth's atmosphere is richest in
(a) ultraviolet (b) infrared (c) X-rays (d) microwaves
(iv) Ozone is found in
(a) troposphere (b) mesosphere (c) ionosphere (d) stratosphere
(i) Solar radiation is
i. transverse electromagnetic wave
ii. longitudinal electromagnetic waves
iii. both longitudinal and transverse electromagnetic waves
iv. none of these.
(a) Option (i) (b) Option (iv) (c) Option (iii) (d) Option (ii)
(ii) What is the cause of greenhouse effect?
(a) Ultraviolet rays (b) X-rays (c) Infrared rays (d) Radiowaves
(iii) Biological importance of ozone layer is
(a) it stops ultraviolet rays
(b) none of these.
(c) it reflects radiowaves
(d) It layer reduces greenhouse effect
OR
Earth's atmosphere is richest in
(a) ultraviolet (b) infrared (c) X-rays (d) microwaves
(iv) Ozone is found in
(a) troposphere (b) mesosphere (c) ionosphere (d) stratosphere
A charged particle moving in a magnetic field experiences a force that is proportional to the strength of the magnetic field, the component of the velocity that is perpendicular to the magnetic field and the charge of the particle. This force is given by $\vec{\text{F}}=\text{q}(\vec{\text{v}}\times\vec{\text{B}})$ where q is the electric charge of the particle, v is the instantaneous velocity of the particle, and Bis the magnetic field (in tesla). The direction of force is determined by the rules of cross product of two vectors. Force is perpendicular to both velocity and magnetic field. Its direction is same as $\vec{\text{v}}\times\vec{\text{B}}$ if q is positive and opposite of $\vec{\text{v}}\times\vec{\text{B}}$ if q is negative. The force is always perpendicular to both the velocity of the particle and the magnetic field that created it. Because the magnetic force is always perpendicular to the motion, the magnetic field can do no work on an isolated charge. It can only do work indirectly, via the electric field generated by a changing magnetic field.
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- When a magnetic field is applied on a stationary electron, it:
- Remains stationary.
- Spins about its own axis.
- Moves in the direction of the field.
- Moves perpendicular to the direction of the field.
- A proton is projected with a uniform velocity v along the axis of a current carrying solenoid, then,
- The proton will be accelerated along the axis.
- The proton path will be circular about the axis.
- The proton moves along helical path.
- The proton will continue to move with velocity v along the axis.
- A charged particle experiences magnetic force in the presence of magnetic field. Which of the following statement is correct?
- The particle is stationary and magnetic field is perpendicular.
- The particle is moving and magnetic field is perpendicular to the velocity.
- The particle is stationary and magnetic field is parallel.
- The particle is moving and magnetic field is parallel to velocity.
- A charge q moves with a velocity $2m\ s^{-1}$ along x-axis in a uniform magnetic field $\vec{\text{F}}=(\vec{\text{i}}+2\vec{\text{j}}+3\vec{\text{k}})\text{T,}$ charge will experience a force.
- In z-y plane.
- Along -y axis.
- Along +z axis.
- Along -z axis.
- Moving charge will produce.
- Electric field only.
- Magnetic field only.
- Both electric and magnetic field.
- None of these.
Two blocks of unequal masses are tied by a spring. The blocks are pulled stretching the spring slightly and the system is released on a frictionless horizontal platform. Are the forces due to the spring on the two blocks equal and opposite? If yes, is it an example of Newton's third law?
A stationary charge produces only an electrostatic field while a charge in uniform motion produces a magnetic field, that does not change with time. An oscillating charge is an example of accelerating charge. It produces an oscillating magnetic field, which in turn produces an oscillating electric fields and so on. The oscillating electric and magnetic fields regenerate each other as a wave which propagates through space.
$(i).$ Magnetic field in a plane electromagnetic wave is given by $\vec{B}= B _0 \sin ( kx +\omega t ) \hat{j} T$Expression for corresponding electric field will be (Where c is speed of light.)
$(a) \vec{E}= B _0 c \sin ( kx +\omega t ) \hat{k} V / m$
$(b) \vec{E}=- B _0 c \sin ( kx -\omega t ) \hat{k} V / m$
$(c) \vec{E}=- B _0 c \sin ( kx +\omega t ) \hat{k} V / m$
$(d) \vec{E}=\frac{B_0}{c} \sin ( kx +\omega t ) \hat{k} V / m$
$(ii)$ The electric field component of a monochromatic radiation is given by $\vec{E}=2 E _0 \hat{i} \cos kz \cos \omega t$. Its magnetic field $\vec{B}$ is then given by
$(a) -\frac{2 E_0}{c} \hat{j} \sin kz \sin \omega t$
$(b) \frac{2 E_0}{c} \hat{j} \sin kz \sin \omega t$
$(c) \frac{2 E_0}{c} \hat{j} \sin kz \cos \omega t$
$(d) \frac{2 E_0}{c} \hat{j} \cos kz \cos \omega t$
$(iii)$ A plane em wave of frequency $25 \ MHz$ travels in a free space along $x -$direction. At a particular point in space and time, $E =(6.3 \hat{j}) V / m$. What is magnetic field at that time?
$(a) \ 0.089 \mu T$
$(b) \ 0.124 \mu T$
$(c) \ 0.021 \mu T$
$(d) \ 0.095 \mu T$
OR
A plane electromagnetic wave travels in free space along $x-$axis. At a particular point in space, the electric field along $y$-axis is $9.3 V m ^{-1}$. The magnetic induction $(B)$ along $z -$axis is
$(a) \ 3.1 \times 10^{-8} T$
$(b) \ 3 \times 10^{-5} T$
$(c) \ 3 \times 10^{-6} T$
$(d) \ 9.3 \times 10^{-6} T$
$(iv)$ A plane electromagnetic wave travelling along the $x-$direction has a wavelength of $3 \ mm$ . The variation in the electric field occurs in the $y-$direction with an amptitude $66 V m ^{-1}$. The equations for the electric and magnetic fields as a function of $x$ and $t$ are respectively
$ \text { a) } E_y =11 \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right), \text { b) } E_y =66 \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right),$
$B_y =11 \times 10^{-7} \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right) B_z =2.2 \times 10^{-7} \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right)$
$\text { c) } E_x =33 \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right), \text { d) } E_y =33 \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right),$
$B_x =11 \times 10^{-7} \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right) B_z =1.1 \times 10^{-7} \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right)$
→$(i).$ Magnetic field in a plane electromagnetic wave is given by $\vec{B}= B _0 \sin ( kx +\omega t ) \hat{j} T$Expression for corresponding electric field will be (Where c is speed of light.)
$(a) \vec{E}= B _0 c \sin ( kx +\omega t ) \hat{k} V / m$
$(b) \vec{E}=- B _0 c \sin ( kx -\omega t ) \hat{k} V / m$
$(c) \vec{E}=- B _0 c \sin ( kx +\omega t ) \hat{k} V / m$
$(d) \vec{E}=\frac{B_0}{c} \sin ( kx +\omega t ) \hat{k} V / m$
$(ii)$ The electric field component of a monochromatic radiation is given by $\vec{E}=2 E _0 \hat{i} \cos kz \cos \omega t$. Its magnetic field $\vec{B}$ is then given by
$(a) -\frac{2 E_0}{c} \hat{j} \sin kz \sin \omega t$
$(b) \frac{2 E_0}{c} \hat{j} \sin kz \sin \omega t$
$(c) \frac{2 E_0}{c} \hat{j} \sin kz \cos \omega t$
$(d) \frac{2 E_0}{c} \hat{j} \cos kz \cos \omega t$
$(iii)$ A plane em wave of frequency $25 \ MHz$ travels in a free space along $x -$direction. At a particular point in space and time, $E =(6.3 \hat{j}) V / m$. What is magnetic field at that time?
$(a) \ 0.089 \mu T$
$(b) \ 0.124 \mu T$
$(c) \ 0.021 \mu T$
$(d) \ 0.095 \mu T$
OR
A plane electromagnetic wave travels in free space along $x-$axis. At a particular point in space, the electric field along $y$-axis is $9.3 V m ^{-1}$. The magnetic induction $(B)$ along $z -$axis is
$(a) \ 3.1 \times 10^{-8} T$
$(b) \ 3 \times 10^{-5} T$
$(c) \ 3 \times 10^{-6} T$
$(d) \ 9.3 \times 10^{-6} T$
$(iv)$ A plane electromagnetic wave travelling along the $x-$direction has a wavelength of $3 \ mm$ . The variation in the electric field occurs in the $y-$direction with an amptitude $66 V m ^{-1}$. The equations for the electric and magnetic fields as a function of $x$ and $t$ are respectively
$ \text { a) } E_y =11 \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right), \text { b) } E_y =66 \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right),$
$B_y =11 \times 10^{-7} \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right) B_z =2.2 \times 10^{-7} \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right)$
$\text { c) } E_x =33 \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right), \text { d) } E_y =33 \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right),$
$B_x =11 \times 10^{-7} \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right) B_z =1.1 \times 10^{-7} \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right)$
Draw a graph showing the change in potential corresponding to the change in distance from a point charge. For the charged system shown in the figure, prove that the potential difference between points $A$ and $B$ is
→Calculate the intensity of the electric field due to the helium nucleus at a distance of $1Å$ from it.
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A bar magnet makes 40 oscillations per minute in an oscillation magnetometer. An identical magnet is demagnetized completely and is placed over the magnet in the magnetometer. Find the time taken for 40 oscillations by this combination. Neglect any induced magnetism.
In the study of Geiger-Marsdon experiment on scattering of α particles by a thin foil of gold, draw the trajectory ofα−particles in the Coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study. From the relation $R = R_0\ A^{1/3},$ where $R_0$ is constant and A is the mass number of the nucleus, show that nuclear matter density is independent of A.
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