E = mc²
E = Δmc²
λ = h/(mv)
R = ρL/A
ρ = m/V
F = GmM/r²
v = u + at
K = (1/2)mv²
P = ΔE/Δt
ΔE = Q + W
Q = mcΔT
W = F × d
d = vt
T = 2π √(l/g)
f = 1/T
λ = v/f
v = √(2gh)
g = Gm/r²
Δp = γ × ΔV
γ = (nRT)/(PV)
n = PV/(RT)
R = 8.314 J/mol·K
T₉₂ = (3/2) × (k_B) × T
k_B = 1.38 × 10⁻²³ J/K
N = N₀ × e^(-λt)
λ = ln(2)/t₁/₂
t₁/₂ = ln(2)/λ
A = λN
N = N₀ × (1/2)^(t/t₁/₂)

🪤 The 5 Mistakes That Cost Marks

Not using the correct units for physical quantities
Forgetting to convert units before plugging into formulas
Not considering the sign conventions for physical quantities
Not using the correct equation for a given situation
Not checking the units of the final answer

✏️ 3 Solved PYQs

Question 1: A nucleus of mass m and charge q is at rest and splits into two nuclei of masses m₁ and m₂ and charges q₁ and q₂. If the kinetic energy of the first nucleus is K₁ and that of the second nucleus is K₂, find the ratio of their kinetic energies. Step 1: Apply conservation of momentum to find the ratio of velocities Steps 2: Use the equation for kinetic energy to find the ratio of kinetic energies Answer: K₁/K₂ = m₂/m₁
Question 2: A radioactive substance has a half-life of 10 years. If 100 g of the substance is left after 20 years, find the initial mass of the substance. Step 1: Use the equation for radioactive decay to find the ratio of initial and final masses Step 2: Plug ∈ the given values to find the initial mass Answer: 400 g
Question 3: A nucleus of ²³⁸U undergoes α decay. Find the kinetic energy of the α particle. Step 1: Find the mass defect of the reaction Step 2: Use the equation E = mc² to find the kinetic energy of the α particle Answer: 4.2 MeV

🧠 The One Thing Most Students Get Wrong

Most students get the concept of nuclear binding energy wrong.
Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons.
It is not the energy released when a nucleus is formed.
The correct equation for nuclear binding energy is ΔE = (Z∓ + Nmn - m)/(Z + N) × c²
Where Z is the number of protons, N is the number of neutrons, ∓ is the mass of a proton, mn is the mass of a neutron, and m is the mass of the nucleus.

👁️ Ayush's Note

To solve problems related to nuclei, always start by identifying the given quantities and the unknown quantities.
Use the equations for conservation of energy, momentum, and charge to find the unknown quantities.
Always check the units of the final answer.
Practice as many problems as possible to develop problem-solving skills.
For JEE Advanced and NEET, focus on solving problems related to nuclear reactions, radioactive decay, and nuclear binding energy.
Use shortcuts like the equation for kinetic energy and the equation for radioactive decay to save time.

🔁 Last 5 Minutes Box

Last 5 minutes revision:
- Nuclear binding energy: ΔE = (Z∓ + Nmn - m)/(Z + N) × c²
- Radioactive decay: N = N₀ × e^(-λt)
- Kinetic energy: K = (1/2)mv²
- Conservation of energy: ΔE = Q + W
- Conservation of momentum: p = mv

📝 Practice MCQs

1. What is the binding energy of a nucleus of ⁴He?

A) 28.3 MeV

B) 30.4 MeV

C) 32.5 MeV

D) 34.6 MeV

Answer: A) 28.3 MeV.

2. A radioactive substance has a half-life of 5 years. If 50 g of the substance is left after 10 years, find the initial mass of the substance.

A) 100 g

B) 200 g

C) 400 g

D) 800 g

Answer: B) 200 g.

3. What is the kinetic energy of an α particle emitted by a nucleus of ²³⁸U?

A) 4.2 MeV

B) 5.5 MeV

C) 6.8 MeV

D) 8.1 MeV

Answer: A) 4.2 MeV.

4. What is the equation for nuclear binding energy?

A) ΔE = (Z∓ + Nmn - m)/(Z + N) × c²

B) ΔE = (Z∓ + Nmn + m)/(Z + N) × c²

C) ΔE = (Z∓ - Nmn - m)/(Z + N) × c²

D) ΔE = (Z∓ - Nmn + m)/(Z + N) × c²

Answer: A) ΔE = (Z∓ + Nmn - m)/(Z + N) × c².

5. What is the ratio of the kinetic energies of two nuclei of masses m₁ and m₂?

A) K₁/K₂ = m₁/m₂

B) K₁/K₂ = m₂/m₁

C) K₁/K₂ = (m₁/m₂)²

D) K₁/K₂ = (m₂/m₁)²

Answer: B) K₁/K₂ = m₂/m₁.

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This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides:

E = mc²
E = Δmc²
λ = h/(mv)
R = ρL/A
ρ = m/V
F = GmM/r²
v = u + at
K = (1/2)mv²
P = ΔE/Δt
ΔE = Q + W
Q = mcΔT
W = F × d
d = vt
T = 2π √(l/g)
f = 1/T
λ = v/f
v = √(2gh)
g = Gm/r²
Δp = γ × ΔV
γ = (nRT)/(PV)
n = PV/(RT)
R = 8.314 J/mol·K
T₉₂ = (3/2) × (k_B) × T
k_B = 1.38 × 10⁻²³ J/K
N = N₀ × e^(-λt)
λ = ln(2)/t₁/₂
t₁/₂ = ln(2)/λ
A = λN
N = N₀ × (1/2)^(t/t₁/₂)