Physics-
General
Easy

Question

Suppose the potential energy between electron and proton at separation r is given by U equals k log subscript e end subscript invisible function application r, where k is a constant for such a hypothetical hydrogen atom, the energy of nth level is

  1. fraction numerator k over denominator 2 end fraction open square brackets 1 plus log invisible function application open parentheses fraction numerator n to the power of 2 end exponent h to the power of 2 end exponent over denominator 4 pi to the power of 2 end exponent m k end fraction close parentheses close square brackets    
  2. fraction numerator k over denominator 2 end fraction open square brackets 1 plus log invisible function application open parentheses fraction numerator n to the power of 2 end exponent h to the power of 2 end exponent over denominator 2 pi to the power of 2 end exponent m k end fraction close parentheses close square brackets    
  3. k open square brackets 1 plus log invisible function application open parentheses fraction numerator n to the power of 2 end exponent h to the power of 2 end exponent over denominator 4 pi to the power of 2 end exponent m k end fraction close parentheses close square brackets    
  4. k open square brackets 1 plus log invisible function application open parentheses fraction numerator n to the power of 2 end exponent h to the power of 2 end exponent over denominator 2 pi to the power of 2 end exponent m k end fraction close parentheses close square brackets    

The correct answer is: fraction numerator k over denominator 2 end fraction open square brackets 1 plus log invisible function application open parentheses fraction numerator n to the power of 2 end exponent h to the power of 2 end exponent over denominator 4 pi to the power of 2 end exponent m k end fraction close parentheses close square brackets


    F equals fraction numerator negative d v over denominator d r end fraction
    fraction numerator m v to the power of 2 end exponent over denominator r end fraction equals fraction numerator k over denominator r end fraction comma m v r equals n open parentheses fraction numerator n over denominator 2 pi end fraction close parentheses
    E equals v plus fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent

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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
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