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challenging question on functions from the JEE Advanced level:
L
et f(x) = x³ + bx² + cx + d and g(x) = x² + px + q, where b, c, d, p, and q are real numbers. If f(x) = g(f(x)) for all x ∈ R, then find the value of b + c + d + p + q.The correct answer is A) 4.45 × 10^-7 m.
Here's the solution:
1. First, find the velocity of the particle using the equation:
v = √(2qV/m)
where q = charge, V = potential difference, and m = mass.
v = √(2 × 4 × 10^-8 C × 100 V / 1 × 10^-6 kg) = 200 m/s
1. Next, find the de Broglie wavelength using the equation:
λ = h/mv
where h = Planck's constant, m = mass, and v = velocity.
λ = (6.63 × 10^-34 Js) / (1 × 10^-6 kg × 200 m/s) = 4.45 × 10^-7 m
Therefore, the de Broglie wavelength associated with the particle is 4.45 × 10^-7 m.
Here's a JEE Advanced-level question in Physics:
"A charged particle of mass 1 × 10^-6 kg and charge 4 × 10^-8 C is accelerated through a potential difference of 100 V. Find the de Broglie wavelength associated with the particle. (Given: h = 6.63 × 10^-34 Js, me = 9.1 × 10^-31 kg)"
A) 4.45 × 10^-7 m
B) 5.55 × 10^-7 m
C) 6.66 × 10^-7 m
D) 7.77 × 10^-7m
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