A diatomic molecule moving at a speed u absorbs a photon of wavelenght `lambda` and then dissociates into two identical atoms. One of the atoms is found to be moving with a speed v in a direction perpendicualr to the initial direction of motion of the molecule. Take mass of the molecule to be M and calculate the binding energy of the molecule. Assume that momentum of absorbed photon is negligible compared to that of the molecule.
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The energy of a photon is given as, `Delta E`/atom `= 3.03 xx 10^(-19)J "atom"^(-1)` then, the wavelength `(lambda)` of the photon is
Correct Answer - C (c) According to formula =, `E=(hc)/(lambda)(v=(c)/(lambda))` Energy E=hv `3.03xx10^(-19)=(hc)/(lambda)` `lambda=(6.63xx10^(-34)xx3.0xx10^(8))/(3.03xx10^(-19))` `=6.56xx10^(-7) m` `=6.56xx10^(-7)xx10^(9)nm` =`6.56xx10^(2) nm` `=656 nm`
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If `[(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2))]=Alambda^(2)+Blambda+C`, where A, B and C are matrices then find matrices B a
We have `[(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2))]=Alambda^(2)+Blambda+C` Putting `lambda=0`, we get `C=[(1,-2),(1,1)]` Putting `lambda=1`, we get `A+B+C=[(0, -1),(3,0)]` ...(1) Putting `lambda=-1`, we get `A-B+C=[(4,-3),(-3,0)]` Subtracting (2) from (1), we get `2B[(0, -1),(3,0)]-[(4,-3),(-3,0)]=[(-4,2),(6,0)]` `:. B=[(-2,...
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The average speed of nitrogen molecule is v. if the temperature is doubled and nitrogen molecule dissociate into nitrogen atoms completely then new av
`v_(mg)=sqrt((8)/(pi)(RT)/(M))` `N_(2)(g)rarr2N(g)` `((v_(avg))N)/((v_(avg))N_(2))sqrt((28xx2T)/(14xxT))=sqrt(4)=2` `(v_(avg))_(N)=2v`
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A nucleus at rest decays by emitting at `alpha` particle. The de-Broglie wavelenght of emitted `alpha` particle is `lambda=-5.76` femtometer. Mass of
Correct Answer - 227.62u
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A deuterium nucleus at rest absorbs a Gamma ray photon of energy 2.21 MeV and splits into a proton and a neutron. The neutron was found to be at rest
Correct Answer - 1.008968u
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If the equations `4x^(2)-x-1=0` and `3x^(2)+(lambda+mu)x+lambda-mu=0` have a root common, then the rational values of `lambda` and `mu` are
Correct Answer - C `(c )` Roots of `4x^(2)-x-1=0` are irrational. So, one root common implies both roots are common. `:. (4)/(3)=(-1)/(lambda+mu)=(-1)/(lambda-mu)=(-2)/(2lambda)=(0)/(2mu)` So, `lambda=(-3)/(4)`, `mu=0`
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Find all values of `lambda` for which the `(lambda-1)x+(3lambda+1)y+2lambdaz=0(lambda-1)x+(4lambda-2)y+(lambda+3)z=0 2x+(3lambda+1)y+3(lambda-1)z=0` p
Correct Answer - D `(d)` `|{:(lambda-1,3lamda+1,2lambda),(lambda-1,4lambda-2,lambda+3),(2,3lambda+1,3(lambda-1)):}|=0` `implieslambda=0` or `3` If `lambda=0`, the equations become `-x+y=0`, `-x-2y+3z=0` and `2x+y-3z=0`, `:. (x)/(6-3)=(y)/(6-3)=(z)/(-1+4)`
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A hydrogen atom in ground state absorbs a photon of ultraviolet radiation of wavelength `50 nm` Assuming that the entire photon energy is taken up by
Correct Answer - `[11.2eV]`
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A spectroscopic instrument can resolve two nearly wavelength `lambda and lambda = Delta lambda if lambda//Delta lambda` is smaller than `8000` This is
Correct Answer - [38]
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`vec(r ) =(lambda-1) hat(i) + (lambda+1) hat(j) -(lambda+1) hat(k)` vec(r ) =(1-mu) hat(i) + (2mu -1) hat(j) + (mu +2) hat(k).`
Correct Answer - `(5sqrt(2))/(2)` units
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