Physics-
General
Easy

Question

The de-Broglie wavelength of a electron is same as the wavelength of an photon. The K.E. of photon is ´ x ´ times the K.E. of the electron, then ´ x ´ is (M – mass of electron, h - Planck’s constant, C - Velocity of light)

  1. fraction numerator h C over denominator 2 lambda M end fraction    
  2. fraction numerator 2 lambda M C over denominator h end fraction    
  3. fraction numerator 2 lambda C over denominator h M end fraction    
  4. fraction numerator 2 lambda M over denominator C h end fraction    

The correct answer is: fraction numerator 2 lambda M C over denominator h end fraction


    Energy of photon, fraction numerator h v over denominator lambda end fraction equals m v c
    And energy of electron = m c to the power of 2 end exponent
    fraction numerator E subscript 1 end subscript over denominator E subscript 2 end subscript end fraction equals fraction numerator m v c over denominator fraction numerator 1 over denominator 2 end fraction M V to the power of 2 end exponent end fraction equals fraction numerator 2 c over denominator V end fraction
    But lambda equals fraction numerator h over denominator m v end fraction rightwards double arrow v equals fraction numerator h over denominator m lambda end fraction
    rightwards double arrow fraction numerator E subscript 1 end subscript over denominator E subscript 2 end subscript end fraction equals fraction numerator 2 c over denominator n divided by m lambda end fraction equals fraction numerator 2 lambda m c over denominator h end fraction

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    When the pressure is considerably high, Vm will be quite small. The pressure correction fraction numerator a n to the power of 2 end exponent over denominator V subscript m end subscript superscript 2 end superscript end fraction may become negligible and van der Waal’s equation reduces to
    P (Vm – nb) = nRT
    This explains why the PVm, after reaching a minimum value, increases with increase in pressure. For a real gas, PV versus P plot is not linear. Hence r/P or m/PV is not independent of P,. For calculation of r and molecular mass M, we must obtain r/P at P =0. As P ® 0,
    P(V – nb) = nRT
    Þ P V equals n left parenthesis R T plus P b right parenthesis equals fraction numerator m over denominator M end fraction left parenthesis R T plus P b right parenthesis
    P equals fraction numerator m over denominator V end fraction open parentheses fraction numerator R T over denominator M end fraction plus fraction numerator P b over denominator M end fraction close parentheses equals rho open parentheses fraction numerator R T plus P b over denominator M end fraction close parentheses
    \ fraction numerator rho over denominator P end fraction equals fraction numerator M over denominator R T end fraction minus fraction numerator M b over denominator left parenthesis R T right parenthesis to the power of 2 end exponent end fraction P
    The nature of graph plotted for P on x-axis versus r/P on y-axis will be:

    When the pressure is considerably high, Vm will be quite small. The pressure correction fraction numerator a n to the power of 2 end exponent over denominator V subscript m end subscript superscript 2 end superscript end fraction may become negligible and van der Waal’s equation reduces to
    P (Vm – nb) = nRT
    This explains why the PVm, after reaching a minimum value, increases with increase in pressure. For a real gas, PV versus P plot is not linear. Hence r/P or m/PV is not independent of P,. For calculation of r and molecular mass M, we must obtain r/P at P =0. As P ® 0,
    P(V – nb) = nRT
    Þ P V equals n left parenthesis R T plus P b right parenthesis equals fraction numerator m over denominator M end fraction left parenthesis R T plus P b right parenthesis
    P equals fraction numerator m over denominator V end fraction open parentheses fraction numerator R T over denominator M end fraction plus fraction numerator P b over denominator M end fraction close parentheses equals rho open parentheses fraction numerator R T plus P b over denominator M end fraction close parentheses
    \ fraction numerator rho over denominator P end fraction equals fraction numerator M over denominator R T end fraction minus fraction numerator M b over denominator left parenthesis R T right parenthesis to the power of 2 end exponent end fraction P
    The nature of graph plotted for P on x-axis versus r/P on y-axis will be:

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