The saturation current from a thoriated-tungsten cathode at 2000 … - Vidyadip

Question

The saturation current from a thoriated-tungsten cathode at 2000 K is 100 mA . What will be the saturation current for a pure-tungsten cathode of the same surface area operating at the same temperature? The constant A in the Richardson-Dushman equation is $60 \times 10^4 \mathrm{Am}^{-2} \mathrm{~K}^{-2}$ for pure tungsten and $3.0 \times 10^4 \mathrm{Am}^{-2} \mathrm{k}^{-2}$ for thoriated tungsten. The work function of pure tungsten is 4.5 eV and that of thoriated tungsten is 2.6 eV .

✓

Answer

$\text{i}=\text{AST}^2\text{ e}^{\frac{-\phi}{\text{KT}}}$$\text{i}_1=\text{i},\ \text{i}_2=100\text{mA}$
$\text{A}_1=60\times10^4,\ \text{A}_2=3\times10^4$
$\text{S}_1=\text{S},\ \text{S}_2=\text{S}$
$\text{T}_1=2000,\ \text{T}_2=2000$
$\phi_1=4.5\text{eV},\ \phi_2 =2.6\text{eV}$
$\text{i}=(60\times10^{4})(\text{S})\times(2000)^2\frac{-45\times1.6\times10^{-19}}{\text{e}^{1.38\times10^{-23}\times2000}}$
$100=(3\times10^{4})(\text{S})\times(2000)^2\frac{-2.6\times1.6\times10^{-19}}{\text{e}^{1.38\times10^{-23}\times2000}}$
Dividing the equation,
$\Rightarrow\frac{\text{i}}{100}=\text{e}^{\big[\frac{-4.5\times1.6\times10}{1.38\times2}\big(\frac{-2.6\times1.6\times10}{1.38\times20}\big)\big]}$
$\Rightarrow\frac{\text{i}}{100}=20\times\text{e}^{-11.014}$
$\Rightarrow\frac{\text{i}}{100}=20\times0.000016$
$\Rightarrow\text{i}=20\times0.0016=0.0329\text{mA}=33\mu\text{A}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Case study (4 Marks)" from Electric Current through Gases→Electric Current through Gases — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Read the passage given below and answer the following questions from 1 to 5. The scalar product or dot product of any two vectors A and B, denoted as A.B (read A dot B) is defined as $\text{A}\cdot\text{B}=\text{AB}\cos\theta$ Where q is the angle between the two vectors. Since A, B and $\cos\theta$ are scalars, the dot product of A and B is a scalar quantity. Each vector, A and B, has a direction but their scalar product does not have a direction. Following are properties of dot product

the scalar product follows the commutative law: A.B = B.A
Scalar product obeys the distributive law: (B + C) = A.B + A.C Further, A. $(\lambda\text{B})=\lambda(\text{A}\cdot\text{B})$ where $\lambda$ is a real number.
For unit vectors i, j, k we have

i × i = j × j = k × k = 1 and i × j = j × k = k × i = 0 $\text{A}\times\text{A}=\mid\text{A}\parallel\text{A}\mid\cos\theta=\text{A}^2.$ B = 0, if A and B are perpendicular. The work done by the force is defined to be the product of component of the force in the direction of the displacement and the magnitude of this displacement. Thus $\text{W}=(\text{F}\cos\theta)\text{d}=\text{F}\cdot\text{d}$ (We see that if there is no displacement, there is no work done even if the force is large. Work has only magnitude and no direction. Its SI unit is (N m) or joule (J). Thus, When you push hard against a rigid brick wall, the force you exert on the wall does not work. No work is done if:

The displacement is zero.
The force is zero. A block moving on a smooth horizontal table is not acted upon by Horizontal force (since there is no friction), but may undergo a large displacement.
The force and displacement are mutually perpendicular. This is so since, for $\theta=\frac{\pi}{2}$ rad
$\cos\big(\frac{\pi}{2}\big)=\theta.$ For the block moving on a smooth horizontal table, the gravitational force mg does no work since it acts at right angles to the displacement. If we assume that the moon’s orbits around the earth are perfectly circular then the earth’s gravitational force does no work. The moon’s instantaneous displacement is tangential while the earth’s force is radially inwards and $\theta=\frac{\pi}{2}.$

Scalar product A.B = B.A is:

Commutative law
Distributive law
Both a and b
None of these

When force acts in the direction of displacement then work done will be:

Positive
Negative
Both a and b can possible
None of these

Define scalar product. give its properties:

Define work done. Give its SI unit

Write down the conditions for which work done is zero

Why does thermionic emission not take place in non-conductors?

On a winter day, the outside temperature is 0°C and relative humidity 40%. The air from outside comes into a room and is heated to 20°C. What is the relative humidity in the room? The saturation vapour pressure at 0°C is 4.6mm of mercury and at 20°C it is 18mm of mercury.

Read the passage given below and answer the following questions from (i) to (v). Momentum and Newton’s Second Law of Motion Momentum of a body is the quantity of motion possessed by the body. It depends on the mass of the body and the velocity with which it moves. When a bullet is fired by a gun, it can easily pierce human tissue before coming to rest resulting in casualty. The same bullet fired with moderate speed will not cause much damage. The greater the change in momentum in a given time, the greater is the force that needs to be applied. The second law of motion refers to the general situation, where there is a net external force rating on the body.

A satellite in force-free space sweeps stationary interplanetary dust at a rate $\frac{\text{dM}}{\text{dt}}=\text{dv,}$ where M is the mass, v is the dt velocity of satellite and a is a constant. What is the deceleration of the satellite?

$\frac{-2\text{av}^2}{\text{M}}$
$\frac{-\text{av}^2}{\text{M}}$
$\text{-av}^2$
$\frac{\text{av}^2}{\text{M}}$

A body of mass 5 kg is moving with velocity of $\text{v} = (2\hat{\text{i}} + 6\hat{\text{j}}) ms^{-1}$ at t = 0s. After time t = 2s, velocity of body is $(10\hat{\text{i}} + 6\hat{\text{j}}) ms^{-1},$ then change in momentum of body is:

$40\hat{\text{i}}\text{ kg}-\text{ms}^{-1}$
$20\hat{\text{i}}\text{ kg}-\text{ms}^{-1}$
$30\hat{\text{i}} \text{kg}-\text{ms}^{-1}$
$(50\hat{\text{i}}+30\hat{\text{j}})\text{ Kg - ms}^{-1}$

A cricket ball of mass 0.25kg with speed 10m/ s collides with a bat and returns with same speed with in 0.01s. The force acted on bat is:

25N
50N
250N
500N

A stationary bomb explodes into three pieces. One piece of 2 kg mass moves with a velocity of 8 ms” 1 at right angles to the other piece of mass 1 kg moving with a velocity of 12 ms -1 . If the mass of the third piece is 0.5 kg, then its velocity is:

$10ms^{-1}$
$20ms^{-1}$
$30ms^{-1}$
$AOms^{-1}$

A force of 10 N acts on a body of mass 0.5kg for 0.25s starting from rest. What is its momentum now?

0.25 N/ s
2.5 N/ s
0.5 N/ s
0.75 N/ s

After a good meal at a party you wash your hands and find that you have forgotten to bring your handkerchief. You shake your hands vigorously to remove the water as much as you can. Why is water removed in this process?

Read the passage given below and answer the following questions from 1 to 5. The cross product of two vectors is given by Vector C = A × B. The magnitude of the vector defined from cross product of two vectors is equal to product of magnitudes of the vectors and sine of angle between the vectors. Direction of the vectors is given by right hand corkscrew rule and is perpendicular to the plane containing the vectors. $\therefore\mid\text{vector}\text{C}\mid=\text{AB}\sin\theta$ and $ \text{Vector}\ \text{C}=\text{AB}\sinθ\text{n}$ Where, cap n is the unit vector perpendicular to the plane containing the vectors A and B. Following are properties of vector product

Cross product does not obey commutative law. But its magnitude obeys commutative low.
$\overrightarrow{\text{A}}\times\overrightarrow{\text{B}}\neq\overrightarrow{\text{B}}\times\overrightarrow{\text{A}}\Rightarrow(\overrightarrow{\text{A}}\times\overrightarrow{\text{B}})$

$=-(\overrightarrow{\text{B}}\times\overrightarrow{\text{A}}),\mid\overrightarrow{\text{A}}\times\overrightarrow{\text{B}}\mid=\mid\overrightarrow{\text{B}}\times\overrightarrow{\text{A}}\mid$

It obeys distributive law

$\overrightarrow{\text{A}}\times(\overrightarrow{\text{B}}\times\overrightarrow{\text{C}})=\overrightarrow{\text{A}}\times\overrightarrow{\text{B}}+\overrightarrow{\text{A}}\times\overrightarrow{\text{C}}$

The magnitude cross product of two vectors which are parallel is zero. Since θ = 0;

$\text{vector}\mid\text{A}\times\text{B}\mid=\text{AB}\sin\theta\circ= 0$

For perpendicular vectors, $ \theta=90\circ,\text{vector}\mid\text{A}\times\text{B}\mid=\text{AB}\sin90\circ\mid\text{cap}\ \text{n}\mid=\text{AB}$

î x î = ĵ x ĵ = ƙ x ƙ = 0
î x ĵ = ƙ; ĵ x ƙ = î; ƙ x î = ĵ
ĵ x î = – (î x ĵ) = – ƙ; ƙ x ĵ = – (ĵ x ƙ) = – î ; î x ƙ = – (ƙ x î) = – ĵ

The expression for a × b can be put in a determinant form which is easy to remember

$\overrightarrow{\text{a}}\times\overrightarrow{\text{b}}=\begin{vmatrix}\overrightarrow{\text{i}}&\overrightarrow{\text{j}}&\overrightarrow{\text{k}} \\\text{a}_{\text{x}} & \text{a}_{\text{y}}&\text{a}_{\text{z}}\\ \text{b}_{\text{x}} &\text{b}_{\text{y}}&\text{b}_\text{z}\end{vmatrix}$
Answer the following questions from above case study.

If θ is angle between two vectors then resultant vector is maximum when θ is:

0
90
180
None of these

Cross product is operation performed between:

Two scalar numbers
One scalar other vector
2 vectors
None of these

Define cross product of two vectors:

State right hand screw rule for finding out direction of resultant after cross product of two vectors.

Give properties of cross product of parallel vector.

Why is the linear portion of the triode characteristic chosen to operate the triode as an amplifier?

Elastic potential energy is Potential energy stored as a result of the deformation of an elastic object, such as the stretching of a spring. It is equal to the work done to stretch the spring, which depends upon the spring constant k as well as the distance stretched

1. If stretch in spring of force constant k is doubled, then the ratio of final to initial forces is:
(a) $4: 1$ (b) $1: 4$ (c) $2: 1$ (d) $1: 2$
2. A light body and a heavy body have the same kinetic energy. which one has greater linear momentum?
(a) light body (b) both heavy and light body (c) Low body (d) heavy body
3. A spring is cut into two equal halves. How is the spring constant of each half affected?
(a) becomes double (b) becomes triple (c) becomes $1 / 4$ th (d) becomes half
OR
When spring is compressed, its potential energy:
(a) fall (b) decrease (c) first increase then decrease (d) increase
4. What type of energy is stored in the spring of a watch?
(a) potential energy (b) Electrical energy (c) mechanical energy (d) kinetic energy

→

The dynamic plate resistance of a triode value is $10\text{k}\Omega$ Find the change in the plate current if the plate voltage is changed from 200V to 220V.

Read the passage given below and answer the following questions from 1 to 5. The kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is $\text{K}=\frac{1}{2}\times\text{mv}^2=\frac{1}{2}\text{v}.\text{v}$ Kinetic energy is a scalar quantity. The kinetic energy of an object is a measure of the work and The energy possessed by an object is thus measured in terms of its capacity of doing work. The unit of energy is, therefore, the same as that of work, that is, joule (J). Work energy theorem: The change in kinetic energy of a particle is equal to the work done on it by the net force. Mathematically $K_f - K_i = W$ Where Ki and Kf are respectively the initial and final kinetic energies of the object. Work refers to the force and the displacement over which it acts. Work is done by a force on the body over a certain displacement.

Kinetic energy is:

Scalar quantity
Vector quantity
None of these

Which of the following has same unit?

Potential energy and work
Kinetic energy and work
Force and weight
All of the above

What is work energy theorem?

Kinetic energy is scalar quantity. Justify the statement.

Give formula for kinetic energy of body.