models

Question 1

equation for number of undecayed nuclei remaining (N)? (N0, λ, t)

Answer 1

N = N0(e^-λt)

where N0 = initial number of undecayed nuclei, λ = decay constant, t = time

Question 2

equation for number of nuclei in sample (n)?

here n = number of nuclei present, in ideal gases n = number of moles and N = number of particles (kind of like number of nuclei)

Answer 2

n = (mass/molar mass) x avogadro’s constant

Question 3

equation for activity of radioactive sample (A)? (λ, N)

Answer 3

A = λN

(dN/dt = -λN, whereas activity = rate of decay of radioactive sample (so A is +))

Question 4

equation for activity of sample at certain point in time (A)? (A0, λ, t)

Answer 4

A = A0(e^-λt)

A0 = initial activity, λ = decay constant, t = time

Question 5

equation for half-life (t 1/2)? (λ)

Answer 5

t 1/2 = ln(2)/λ

Question 6

equation for capacitance (C)? (Q, V)

Answer 6

C = Q/V

Question 7

equation for total work done in charging capacitor (E or W)? (Q, V)

Answer 7

E = 0.5QV

where Q = total charge and V = voltage (energy per unit charge)

Question 8

equation for total work done in charging capacitor (E or W)? (C, V)

Answer 8

E = 0.5CV^2

Question 9

equation for total work done in charging capacitor (E or W)? (Q, C)

Answer 9

E = (Q^2)/2C

Question 10

equation for charge remaining on a discharging capacitor (Q)? (Q0, t, R, C)

Answer 10

Q = Q0(e^-t/RC)

Question 11

equation for current remaining on a discharging/currently on charging capacitor (I)? (I0, t, R, C)

Answer 11

I = I0(e^-t/RC)

Question 12

equation for pd remaining on a discharging capacitor (V)? (V0, t, R, C)

Answer 12

V = V0(e^-t/RC)

Question 13

equation for charge on a charging capacitor (Q)? (Q0, t, R, C)

Answer 13

Q = Q0(1 - e^-t/RC)

Question 14

equation for pd (V) on a charging capacitor? (V0, t, R, C)

Answer 14

V = V0(1 - e^-t/RC)

Question 15

equation for restoring force (F) acting during SHM? (x)

Answer 15

F = -kx

where k = spring constant (when spring is oscillating, it might be smth else sometimes), x = displacement from quilibrium

(also minus bc restoring force acts in opposite direction to displacement)

Question 16

equation for acceleration (a) of pendulum during SHM?

Answer 16

a = (-k/m)x

Question 17

equation for angular frequency (ω)? (T)

Answer 17

ω = 2π/T

where T = time period (time taken for one complete oscillation)

(for ω, treat 1 oscillation as whole circle of 2π radians)

Question 18

equation for angular frequency (ω)? (f)

Answer 18

ω = 2πf

Question 19

equation for displacement (x) in SHM (when starting from the side)? (ω, A, f, t)

Answer 19

x = Acos(ωt)
or
x = Acos(2πft)

Question 20

equation for displacement (x) in SHM (when starting from the midpoint)? (ω, A, f, t)

Answer 20

x = Asin(ωt)
or
x = Asin(2πft)

Question 21

equation for velocity (v) in SHM (when starting from side)? (ω, A, f, t)

Answer 21

v = -ωAsin(ωt)

Question 22

equation for velocity (v) in SHM (when starting from midpoint)? (ω, A, f, t)

Answer 22

v = ωAcos(ωt)

Question 23

equation for v max (when starting from side)? (ω, A)

Answer 23

v max = ωA

Question 24

what is the equation for acceleration (a) in SHM (when starting from the side)? (ω, A, t)

Answer 24

a = -(ω^2)Acos(ωt)

Question 25

what is the equation for acceleration (a) in SHM (when starting from the midpoint)? (ω, A, t)

Answer 25

a = -(ω^2)Asin(ωt)

Question 26

equation for a (a) in SHM (when starting from the side)? (ω, x)

Answer 26

a = -(ω^2)x

where ω = angular frequency and x = displacement

Question 27

equation for maximum kinetic energy (KE max) for SHM pendulum? (m, ω, A)

Answer 27

KE max = 0.5m(ω^2)(A^2)
OR
KE max = 0.5k(A^2)

Question 28

maximum elastic potential energy (EPE max) for SHM? (x, A)

Answer 28

EPE max = 0.5k(x max^2)
OR
EPE max = 0.5k(A^2)

Question 29

equation for time period (T) of mass-spring system in SHM? (m, k)

Answer 29

T = 2π√(m/k)

where m = mass and k = spring constant of spring

Question 30

equation for time period (T) of oscillation of pendulum in SHM? (L, g)

Answer 30

T = 2π√(L/g)

where L = length of string and g = g

Question 31

equation to show decrease of SHM displacement due to damping is exponential? (ratios basically)

Answer 31

x1:x2 = x2:x3 = x3:x4

(ratios of decreasing displacements must all be same if exponential)

Question 32

equation for number of nuclei remaining (N) after certain number of half lives? (N0, no. of half lives passed)

Answer 32

N = N0 x (0.5)^no. of half lives passed

Question 33

equation for mass of radioactive sample after time t?

Answer 33

m = m0(e^-λt)

Question 34

equation for count rate of radioactive sample after time t has passed?

Answer 34

C = C0(e^-λt)