Solution - Career Point

PHYSICS FUNDAMENTAL FOR IIT-JEEAtomic Structure, X-Ray & Radio ActivityKEY CONCEPTS & PROBLEM SOLVING STRATEGYAtomic Structure :According to Neil Bohr's hypothesis is the angularmomentum of an electron is quantised.n = ∞n = 7n = 6n = 5n = 4⎛mvr = n ⎜⎝2πr = nλh2π⎟⎠⎞or L = nh2πh ⎛ c ⎞ zv n = Zn = ⎜ ⎟ × ms–12πmr⎝137⎠ n⎛2r n = ⎜h2⎝ 4πmke2⎞⎟⎠n 2Z⎛ ⎞f n = ⎜ke 2 ⎟1 6.58×× = ⎝ hr ⎠ n n10n 2= 0.529 Å where k =Z15Hz14πε1 ke 2 Z − ke 2ke 2K.E. = ; P.E. = × Z; T.E. = – × Z2 rr2rn = 3n = 22−13.6ZT.E. = ev/atom where –13.62n= Ionisation energy+P.E.⇒ +T.E. = = – K.E.2Note : If dielectric medium is present then ε r has tobe taken into consideration.v 1 = = v =c λ⎡= RZ 2 1 1⎥ ⎥ ⎤⎢ −2 22⎢⎣n1 n ⎦K βK γK δL γL β4 2me z ⎡ 1 1⎥ ⎥ ⎤⎢ −2 3 2 28ε0h c ⎢⎣n1n 2 ⎦L αBalmer(Visible)p mv= = h hPaschen(I.R.)PfundBrackett (I.R.)(I.R.)Limiting line of Lyman seriesn = 1Lyman Series(U.V. rays)–0.85 eV–1.5 eV–3.4 eV–13.6 eV0The maximum number of electrons that can beaccommodated in an orbit is 2n 2 .X-rays :When fast moving electron strikes a hard metal,X-rays are produced. When the number of electronsstriking the target metal increases, the intensity of X-rays increases. When the accelerating voltage/kineticenergy of electron increases λ min decreases. X-rayshave the following properties :(a) Radiations of short wavelength (0.01 Å – 10Å);high pentrating power; having a speed of 3 × 10 8 m/sin vacuum.IntensityContinuous spectrum(Varies & depends onaccelerating voltage)λ minhc(b) λ min = = eVK βK αL γhcK. ECharacteristic spectrum(fixed for a target material)L βL α=λ12400 ÅV1(c) = R(Z – b)2 ⎡ 1 ⎤λ⎢1− ⎥⎣ n 2⎦b = 1 for k-line transfer of electron(d) Moseley law ν = a(z – b)R = R 0 A 1/3 where R 0 = 1.2 × 10 –15 mR = radius of nucleus of mass number A.* Nucleus density is of the order of 10 17 kg/m 3Isomers are nuclides which have identical atomicnumber and mass number but differ in their energystates.Nuclear binding energy ∆mc 2=NucleonAwhere ∆m = mass defect2[Zmp+ (A − Z)mn− M]c=AXtraEdge for IIT-JEE 27 APRIL 2010