Ok, I have few questions which I solved but the answers in he book do not match with the ones that I got.
Q1. The de-Brogile wavelength of a neutron at 927 degree C is {lambda}. What will be its wavelength at 27 degree C? I got 2 {lambda}, book says {lambda}/2
Q2. The distance between interatomic latice planes is 10A. What will be the maximum wavelength of X-Ray diffracted by the crystals? My ans 20A, book says 40A.
Q3. A parallel plate capacitor with plate area 'A' and separation 'd' is filled with dielectics k1 and k2 of equal thickness. What will its capacitance be? I have no idea about this one.
Q4. Two rain drops falling through air have radii in the ratio 2:3. What will be the ratio of their terminal velocity?
Q1. To solve this question, we need to use de Broglie's equation, which relates the wavelength of a particle to its momentum. The equation is given as:
λ = h / p
Where λ is the wavelength, h is the Planck's constant, and p is the momentum of the particle.
Given that the de Broglie wavelength of the neutron at 927 degrees Celsius is λ, and we need to find its wavelength at 27 degrees Celsius. Since the momentum of the neutron will remain the same in both cases, the wavelength will also remain the same. Therefore, the answer should be λ, not 2λ. It seems like there might be an error in the book.
Q2. In this question, we need to use Bragg's Law, which describes the diffraction of X-rays by crystal lattice planes. The equation is given as:
nλ = 2d sin(θ)
Where n is the order of the diffraction, λ is the wavelength, d is the distance between adjacent lattice planes, and θ is the angle of incidence.
To find the maximum wavelength, we need to consider the first-order diffraction (n=1) for which sin(θ) will be at its maximum value of 1. Therefore, the equation simplifies to:
λ = 2d
Given that the distance between interatomic lattice planes (d) is 10A, the maximum wavelength (λ) will be 2d = 2 * 10A = 20A. So, your answer of 20A is correct, but the book's answer of 40A seems to be incorrect.
Q3. To find the capacitance of the parallel plate capacitor filled with two dielectrics, we can use the following formula:
C = (k1 * k2 * ε0 * A) / (d1 * k1 + d2 * k2)
Where C is the capacitance, k1 and k2 are the relative permittivities of the two dielectrics, ε0 is the permittivity of free space, A is the area of the plates, d1 and d2 are the thicknesses of the dielectrics.
Since the thickness of the two dielectrics is equal, let's say d, the formula can be simplified to:
C = (k1 * k2 * ε0 * A) / (2d)
So, the capacitance of the parallel plate capacitor filled with dielectrics k1 and k2 of equal thickness will be (k1 * k2 * ε0 * A) / (2d).
Q4. The terminal velocity of an object falling through a fluid depends on various factors, including the radius of the object. According to Stoke's Law, the terminal velocity (Vt) is given by:
Vt ∝ r^2
Where r is the radius of the object.
Given that the radii of the two raindrops are in the ratio 2:3, let's assume their radii to be 2r and 3r respectively.
The ratio of their terminal velocities (Vt1/Vt2) will be:
(Vt1/Vt2) = (r1^2)/(r2^2) = (2r)^2/(3r)^2 = 4/9
So, the ratio of their terminal velocities is 4:9.