यदि |a_(i)| lt 1, Lambda_(i) ge 0 for i=1,2,……n और Lambda_(1)+lambda_(2)+…….+lambda_(n)=1, फिर...

If |a_(i)| lt 1, lambda_(i) ge 0 for i=1,2,……n and lambda_(1)+lambda_(2)+…….+lambda_(n)=1 , then the value of |lambda_(1)a_(1)+lambda_(2)a_(2)+…….+lambda_(n)a_(n)| is

If |a_i| < 1,lamda_i geq0 for i=1,2,3,...,n and lambda_1+lamda_2+...lambda_n=1 then the value of |lambda_1 a_1+lambda_2 a_2+......+lambda_n a_n| is

Let K_(1) be the maximum kinetic energy of photoelectrons emitted by a light of wavelength lambda_(1) and K_(2) corresponding to lambda_( 2). If lambda_(1) = 2lambda_(2) , then

A block body at temperature T radiates same amount of energy in the wavelength range lambda_(1) to lambda_(1)+Deltalambda and lambda_(2) to lambda_(2)+Deltalambda . It is given that Deltaltltlambda_(1) or lambda_(2) and lambda_(2)gtlambda_(1) . Prove that (b)/(lambda_(1))gtTgt(b)/(lambda_(2)) where b is Wien's constant.

Cut off potentials for a metal in photoelectric effect for light of wavelength lambda_(1), lambda_(2) and lambda_(3) is found to be V_(1), V_(2) and V_(3) volts if V_(1), V_(2) and V_(3) are in Arithmetic Progression and lambda_(1), lambda_(2) and lambda_(3) will be :

Let be the maximum kinetic energy of photoelectrons emitted by light of wavelength lambda_(1) and lambda_(2) correspondingto wavelength lambda_(2) . If lambda_(1) = 2lambda_(2) then:

When radiations of wavelength lambda_(1), lambda_(2) (= 0.6 lambda_(1)), lambda_(3) (= 4lambda_(2)) and lambda_(4) are incident on a metal plate, photoelectrons with maximum kinetic energy of – 5.2 eV are emitted for lambda_(1), 12 eV are emitted for lambda_(2), 0.95 eV are emitted for lambda_(4) and no electron is emitted for l3. It is known that a hydrogen like atom (atomic number Z) in a higher excited state of quantum number n can make a transition to first excited state by successively emitting two photons of wavelength lambda1 and lambda_(2) respectively. Alternatively, the atom from same excited state can make a transition to the second excited state by successively emitting two photons of wavelength lambda_(3) and lambda_(4) respectively. (a) Find the work function of the metal. (b) Find the values of n and Z for the atom.