if an electron is revolving in its bohr orbit having bohr radius of `0.529Å`, then the radius of third orbit is
A. `4234Å`
B. `4496Å`
C. `4.761Å`
D. `5125nm`
1 Answers
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The radius of the orbit of an electron in a Hydrogen-like atom is `4.5 a_(0)`, where `a_(0)` is the Bohr radius. Its orbital angular momemtum is `(3h)
Correct Answer - A::C Angular momentum `=(nh)/(2pi)=(3h)/(2pi)implies n=3` Also `r=n^(2)/2 a_(0) implies (9a_(0))/2=3^(2)/Z a_(0) implies Z=2` For de-excitation `1/lambda=Rz^(2) [1/n_(1)^(2)-1/n_(2)^(2)]=4R[1/n_(1)^(2)-1/n_(2)^(2)]` For `n=3` to `n=1` : `1/lambda=4R[1/1-1/9] implies lambda=9/(32R)` For `n=3` to...
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In the nth orbit, the energy of an electron `E_(n)= -( 13.6)/(n^(2)) eV` for hydrogen atom. The energy rquired to take the electron from first orbit t
Correct Answer - A For n=2, using, `E_(n)=(-13.6eV)/(n^(2))E_(2)=-(13.6)/((2)^(2))=-3.4 eV` For n=1,`E_(1)=-13.6 eV` `:. " " E_(1rarr2)=-3.4-(-13.6)=10.2ev`
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The velocity of an electron in the first orbit of H-atom is v. The velocity of an electron in the 2nd orbit
Correct Answer - C `vprop(Z)/(n)` since Z and n both have become twice, velocity of electron in second orbit of `H^(+)` will be v.
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Electrons are revolving around the nucleus in `n_(1^(th))` orbit of an atom, have atomic number `Z_1`, and in the `n_2` orbit of other atom, have atom
Correct Answer - A,B,D `L_1/L_2=(mv_1r_1)/(mv_2r_2)=(Z_1/n_1xxn_1^2/Z_1)/(Z_2/n_2xxn_2^2/Z_2)=n_1/n_2implies P_1/P_2(mv_1)/(mv_2)=(Z_1/n_1)/(Z_2/n_2)=(Z_1n_2)/(Z_2n_1)` `(f_1)/(f_2) =(v_1/(2pir_1))/(v_2/(2pir_2))=(Z_1/n_1xxZ_1/n_1^2)/(Z_2/n_2xxZ_2/n_2^2)=(Z_1/Z_2)^2.(n_2/n_1)^3implies (K.E._1)/(K.E._2)=(1/2mv_1^2)/(1/2mv_2^2)=(Z_1/Z_2)^2xx(n_2/n_1)^2=((Z_1n_2)/(Z_2n_1))^2` `(K.E_1)/(K.E_2)=(1/2(KZ_1e^2)/r_1)/(1/2(KZ_2e^2)/r_2)=(Z_1/n_1^2.Z_1)/(Z_2.Z_2/n_2^2)=(Z_1/Z_2.n_2/n_1)^2`
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the wavelength of radiation emitted is `lambda_0` when an electron jumps. From the third to second orbit of hydrogen atom. For the electron jumping fr
Correct Answer - B `(lambda)/(lambda_0)=([(1)/(2^2)-(1)/(3^2)])/([(1)/(2^2)-(1)/(4^2)])=(5)/(36)xx(16)/(3)=(20)/(27)`or `lambda=(20)/(27)lambda_0`
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The electric current I created by the electron in the ground state of H atom bohr model in terms of bohr radius `(a_0)` and velocity of electron in fi
Correct Answer - A In the ground state of hydrogen atom, suppose, `a_0=` bohr radius `v_0=` velocity of electron in first orbit `therefore` time taken by electron to complete one revolution,...
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An electron is revolving in the `n^(th)` orbit of radius `4.2 Å`, then the value of n is `(r-1=0.529 Å)`
Correct Answer - D Since `r_npropn^(2),(r_n)/(r_1)=(n^2)/((1)^2)` `therefore r_n=n^2r_1`or `n^2=(r_n)/(r_1)` `rArrn=sqrt((r_n)/(r_1))=sqrt((4.2)/(0.529))=sqrt(7.939)=2.81approx3`.
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(A) the total energy of an electron revolving in any stationary orbit is negative. (R) energy can have positive or negative values.
Correct Answer - B Energy can have positive or negative values. in the atom. the electrons are bound . The negative energy of the revolving electrons does not allow the electrons...
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A particle revolving in a circular path completes first one third of circumference in 2 sec, while next one third in 1 sec. The average angular veloci
`theta_(1)=(2pi)/(3)and theta_(2)=(2pi)/(3)"total time T"=2+1=3s therefore ltomega_(av)gt(theta_(1)+theta_(2))/(T)=((2pi)/(3)+(2pi)/(3))/(3)=((4pi)/(3))/(3)=(4pi)/(9)"rad/s"`
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The orbit having Bohr radius equal to 1st Bohr orbit of H-atom is :
Correct Answer - D `r_(n)=0.529 n^(2)/Z ` For hydrogen, `n=1` and `Z=1, :. r_(H)=0.529` For `Be^(3+), n=2` and `Z=4, :. r_(Be^(3+))=(0.529xx2^(2))/(4)=0.529` there, (D) is correct option.
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