Inertial & Gravitational Masses

INERTIAL AND GRAVITATIONAL MASSES:
(i) Inertial masses :– It is a measure of the ability of a body to oppose the production of acceleration in it by an external force. It also measure inertia of a body.
Let F be applied force on a body which produces an acceleration a
Then, F = ma
m = F/a
(i) Gravity has no effect on the inertial mass of the body
(ii) Inertial mass does not depends upon the size, shape and state of the body
(iii) Inertial mass of a body does not depend upon on the presence or absence of other bodies near it.
(iv) Inertial mass of a body is directly proportional to the quantity of matter contained in the body.
(v) Inertial mass of the body increases with increase in velocity.
m= mo/(1-v2/c2)1/2
Where mo is mass of a body at rest
v is velocity of the body
c is the velocity of the light in vacuum.
Gravitation of Mass :–
It is defined as mass of body which determines the magnitude of gravitational pull between the body and the earth. Let F be the gravitational force on a body of mass m due to earth
Then F = GMm/R2
Where R is the radius of earth
M is the mass of earth
m = FR2/GM
The mass of body determined in this way is the gravitational mass of the body.
Gravitational mass is same as inertial mass in all respect, except in the method of their measurement.

Moseley’s Law & Diffraction of X- Rays

♦ Learn about : Moseley’s Law , Diffraction of X- Rays & Uses of X – Rays ♦
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Moseley studied the characteristic X-ray spectrum of a number of a heavy elements, and observed a simple relationship between them. He found that the spectra of different elements are very similar, and with increasing atomic number Z , the spectral lines nearly shift towards shorter wavelength or higher frequencies.

He plotted a graph of the k-series between the square root of frequency (√ν)and atomic number (Z) and found it very approximately to be a straight line.

He therefore concluded that the  square- root of the frequency of a K-line is closely proportional to the atomic number of the element. This is called Moseley’s Law and may be expressed as :

 

Moseley’s Law

a = proportionality constant

b = screening constant

a and b does not depend on the nature of target.

Diffraction of X- Rays :-

Diffraction of X- Rays

(1)  According to Laue the wavelength of X-Rays is very small and the atoms in crystals are arranged in form of three dimensional lattice.

(2) The diffraction of X-Rays is not possible by ordinary grating because the size of grating element is much larger than the wavelength of X-Rays.

(3) Diffraction of X-Rays is possible by the crystals. Because the inter atomic spacing in a crystal lattice is of the order of wavelength of X-Rays.

(4) Diffraction of X-Rays was first verified by laue spots.

(5) Diffraction of X-Rays takes place according to Bragg’s law

  • (a) 2d sin θ = nλ
  • (b) For maximum wavelength nmin = 1

(sin θ)max = 1
λmax = 2d

Uses of X – Rays
(i) In Study of crystal structure

(ii) In Surgery

(iii)  In Medicine

(iv)  In Spying

(v)   In Engineering

(vi)   In Research in the laboratories

(vii)  In Industries

(viii)  In Radiography

Motion of Charged Particle Through Magnetic Field

♦ Study about the Motion of Charged Particle Through Magnetic Field . The path of the particle in the magnetic field is circular ♦

The magnetic force equation gives, for a particle of charge q , mass m , velocity u, magnetic field B ,
Mag field

The radius of the circular path is
Mag field

Note : The figure shows a charged particle , moving in a Straight line , enters a region of magnetic field (field upwards). Once the particle is inside the field region, it experiences a magnetic force qvB . The path of the particle in the magnetic field is circular. Once it leaves the field region, the path becomes a straight line again. Let a screen is placed at a distance D from the centre of the field region. Then, the displacement OP’ , is X = D tanθ . It can be proved that tanθ = qBL/mu

Mag field

Mag field

Notice the difference, that when particle crosses a perpendicular electric field region, and hits the screen, the displacement observed is Y = qELD/mu2 while when it crosses a perpendicular magnetic field region and hits the screen, the displacement is X = qBLD/mu.

Motion of Charged Particle Through Electric Field

♦ Study about the Motion of Charged Particle Through Electric Field . The path of the particle in the Electric  field is parabolic  ♦

Consider a particle of mass m , charge q , moving horizontally with velocity u , as shown in the figure. The charge enters a region between two parallel plates (length L), where an electric field E , as shown exists. Since, there is no horizontal force on the particle , the horizontal component of velocity does not change ,
vx = u at all times . The time spent by the particle in the field region is

t = L/u

electric field

During this time, the particle experiences a vertical force Fy = qE . Due to this force acceleration in
Y-direction is ay = qE/m . In time t , the velocity acquired in Y-direction is

vy = ayt

vy = qEL/mu

The angle θ , at which the particle emerges out of the field (figure) is

tan θ = vy/vx

The velocity with which the particle comes out of the field is

electric field

The path of the particle in this case is parabolic this can be seen as follows. In any time t, the distances traveled by the particle in x, and y direction are

electric field

eliminating t , we get

electric field

y ∝ x2

The path is a parabola.

Photo Electric Effect & Laws of Photo Electric Effect

 ♦ Learn about : Photo Electric Effect : LENARD’S EXPLANATION , EXPERIMENTAL ARRANGEMENT ♦

  • Hertz observed that when ultra violet rays are allowed to fall on negative plate of an electric discharge tube, then conduction takes place more easily. This shows that electrons are ejected from a metal surface when illuminated by light of suitable wavelength .
  • After some time, Hall wach confirmed above observation through his following convincing experiment : His apparatus consists of two zinc plates enclosed in an evacuated quartz tube.

photo-electric-effect

The plates are connected to a battery through a galvanometer (fig.). He noted following observations :

  • When U.V. rays are allowed to fall on the cathode, deflection is produced in the galvanometer i.e., a current flows in the circuit.
  • As soon as rays are stopped, the deflection in the galvanometer becomes zero or current stops.
  • If rays are made to fall on anode then either no current or a very small current flows in the circuit.

LENARD’S EXPLANATION :

(a) He told that when ultraviolet rays fall on cathode electrons are ejected from it which are attracted toward anode or positively charged plate. Hence, the circuit which was incomplete till now, due to air gap between two plates in the tube, gets completed due to flow of electrons and a current starts flowing in the circuit.

  • However, when rays fall on anode, the electrons are again emitted from the plate in the same way as earlier but because of being negatively charged do not reach the cathode i.e., circuit again remains incomplete and the current does not flow.

This phenomenon of emission of electrons from a metallic surface when illuminated by light of appropriate wavelength frequency is known as PHOTO ELECTRIC EFFECT. The electrons emitted in this process are called as photo-electrons and the current produced in the circuit is called as photo-electric current.

Note :-

  • Photo-electric effect is a general phenomenon exhibited by all substances when illuminated by radiations of suitable wavelength. This suitable wavelength is different for substances.
  • Certain alkali-metals e.g. Sodium, Potassium, Calcium etc., show the photo electric effect when visible light (l = 4000 Aº − 7500 Aº) falls on them.
EXPERIMENTAL ARRANGEMENT :

Study of the dependence of maximum kinetic energy and photo electric current.

LENARD’S EXPLANATION

♦ Learn about : Laws of Photo Electric Effect : Intensity effect , Frequency effect , Effect of nature of metals , Time-delay effect ♦

(a)Intensity effect : For a given metal, rate of emission of photo-electrons i.e., photo current is directly proportional to the intensity of incident radiation for a given light i.e., bright light always gives more photo-current than a dim one for a given frequency.

(b)Frequency effect : For a given metal, maximum kinetic energy of photo electrons varies linearly with the frequency of incident radiation and is independent of its intensity i.e., blue light will always give more energetic photoelectrons than red, whatever be its intensity.

(c) Effect of nature of metals : If light of different frequencies in turn is incident on a given metal, photo electric effect takes place only if the frequency of incident radiation is more ( or wavelength is less ) than a specific value V0 . This specific value of frequency (V0) is called threshold-frequency or cut-off frequency and depends only on the nature of metal.

So if from a certain metal, green light can emit photo electrons while yellow can not, blue light will emit photo electrons (as VB>VG) while red will not. For PEE ν ≥ ν­0   , λ ≤ λ­0

(d) Time-delay effect : Within the limits of experimental accuracy (about 10–9 s.), there is no time lag between incidence of radiation and emission of photo electrons i.e., as light is incident on the metal photo electrons are emitted.

(e) The rate at which the electrons are emitted from a photocathode is independent of its temperature. This shows that it is different from thermionic emission.

Note : –

  • In accordance with conservation of energy photo electric effect represents conversion of light energy reverse of what happens in an electric bulb.
  • Photo electric effect takes place only if the electron is loosely bound to the metal, i.e., photo-electric effect can never take place with completely free electron.
  • In photo-electric effect all the emitted photo electrons do not have same kinetic energy. The emitted photo electrons have kinetic energy in the range from 0 to a maximum value. Kmax depends both on frequency of incident radiation and nature of metal.
  • With emission of photo electrons the metal will become positively charged and if isolated, photoelectric effect will cease after some time when potential acquired by the metal V is such that eV = Kmax. in this situation any electron emitted by the metal will turn back to it by attractive force and will not escape.
  • The opposite of photo-electric effect i.e. emission of electromagnetic radiation. From a metal when electrons strikes it results in the production of X-rays and is called ‘inverse photo electric effect.
  • Apart from photo electric emission, electrons can also be emitted from a metal by heating (Thermionic – emission), by applying a strong electric field (field emission) or by bombarding it with electrons (secondary emission).
  • Irradiation of a substance by light under specific conditions instead of producing photoelectric effect may increase its electrical conductivity resulting in ‘photo conductive effect’ or may produce an EMF across it resulting in photo Voltaic effect.