The wavelength of `K_(alpha)` X-ray of tungsten is 21.3 pm. It takes 11.3 keV to knock out an electron from the L shell ofa tungsten atom. What should be the minimum accelerating voltage across an X-ray tube having tungsten target which allows production of `k_(alpha)` X-ray ?
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Prove that `tan alpha+2 tan 2 alpha+2^(2)tan^(2)alpha+..............+2^(n-1)tan2^(n-1)alpha+2^(@)cot2^(@)alpha=cotalpha`
We know `tan theta=cot theta-2 cot 2 theta`. Putting `theta=alpha,2alpha,2^(2)alpha,....................` in (i), we get `tan alpha=(cot alpha-2 cot 2alpha)` `2(tan2alpha)=2(cot 2 alpha-2 cot 2 ^(2)alpha)` `2^(2)(tan2^(2)alpha)=2^(2)(cot2^(2)alpha-2cot2^(3)alpha)` `2^(n-1)(tan2^(n-1)alpha)=2^(n-1)(cot2^(n-1)alpha-2cos2^(n)alpha)` Adding, `tan alpha+2tan...
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If `A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))]`, then `A(alpha, beta)^(-1)` is equal to
Correct Answer - A We have, `A(alpha, beta)^(-1)=1/e^(beta) [(e^(beta) cos alpha,-e^(beta) sin alpha,0),(e^(beta) sin alpha,e^(beta) cos alpha,0),(0,0,1)]` `=A(-alpha, -beta)`
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If `alpha, beta, gamma` are three real numbers and `A=[(1,cos (alpha-beta),cos(alpha-gamma)),(cos (beta-alpha),1,cos (beta-gamma)),(cos (gamma-alpha),
Correct Answer - A::B::D `A=[(cos alpha,sin alpha,0),(cos beta,sin beta,0),(cos gamma,sin gamma,0)][(cos alpha,cos beta,cos gamma),(sin alpha,sin beta,sin gamma),(0,0,0)]` Clearly, A is symmetric and `|A|=0`, hence, singular and not invertiable. Also, `A A^(T)...
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If `f(x)=x^(11)+x^9-x^7+x^3+1` and `f(sin^(-1)(sin8)=alpha,alpha` is constant, then `f(tan^(-1)(t a n8)` is equal to `alpha` (b) `alpha-2` (c) `alpha+
Correct Answer - D `f(x) + f(-x) = 2` Now `(sin^(-1) (sin 8)) = 3pi - 8 = y` And `(tan^(-1) (tan 8)) = (8 - 3pi) = -y` Hence, `f(y)...
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The value of `(alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec^2(1/2tan^(-1)(beta/alpha))i se q u a lto` `(alpha+beta)(alpha^2+beta^2)` (b) `
Correct Answer - C `(alpha^(3))/(2) cosec^(2) ((1)/(2) tan^(-1). (alpha)/(beta)) + (beta^(3))/(2) sec^(2) ((1)/(2) tan^(-1).(beta)/(alpha))` `= alpha^(3) (1)/(1 - cos(tan^(-1) ((alpha)/(beta)))) + beta^(3) (1)/(1 + cos (tan^(-1).(beta)/(alpha)))` `= alpha^(3) (1)/(1 -cos (cos^(-1)...
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An X-ray tube has nickel as target. The wavelength difference between the ka X-ray and the cut-off wavelength of continuous X-ray spectrum is 84 pm. F
Correct Answer - `14.8 kV`
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In a X-ray tube, after an electron has been removed from an inner shell of a target atom, an electron from outer shell falls into the vacancy and the
Correct Answer - `E_(k) - 2E_(L)`
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Iron emits `K_alpha` X-ray of energy 6.4 keV and Calcium emits `K_alpha` X-ray of energy 3.69 keV. Calculate the times taken by an iron `K_a` photon a
Correct Answer - [10 us by both]
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The `K_beta` X-ray of argon has a wavelength of 0.36 nm. The minimum energy needed to ionize an argon atom is 16 eV. Find the energy needed to knock o
Correct Answer - `3.47 keV`
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The energy of K-electron in tungsten is -20.0 keV and of an L-electron is -2.0 ke V. Find the wavelength of X-rays emitted when an electron jumps from
Correct Answer - 0.6875 Å
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