Скачать или смотреть PYQ 2020 | CBSE Class 12 Physics | Section -D | 55/4/1 | Previous year Q&A | ICAN Physics Academy

Radioactive Law of Decay

● Radioactive decay is a spontaneous process — no external force is needed.
● Unstable nuclei change by emitting α (alpha), β (beta) or γ (gamma) radiation.
● Let N = number of undecayed atoms at any time t.
● Let λ = decay constant (probability of decay per second).
● Rate of decay is directly proportional to the number of atoms present.
⇒ − dN/dt ∝ N
● Introducing the constant of proportionality λ:
⇒ − dN/dt = λN
● As time increases, N decreases continuously.
● Decay process is random, but follows a definite mathematical law.
● Each radioactive element has its own unique decay constant (λ).
● Decay continues until a stable nucleus is formed.

⏳ Half-Life

● Half-life is the time taken for half of the radioactive atoms in a sample to decay.
● If you start with a number of atoms N₀, after one half-life only N₀/2 atoms remain undecayed.
● After the second half-life → N₀/4 remain.
● After the third half-life → N₀/8 remain, and so on.
● Half-life is represented by the symbol T₁/₂.
● Each radioactive element has a constant and unique half-life (cannot be changed by heat, pressure, or chemical reactions).
● Half-life is independent of the amount of the substance → small or large sample decays in the same ratio.
● Radioactive decay is exponential and occurs at a rate proportional to the number of remaining atoms.
● Half-life helps us measure how fast or slow a substance decays.
● Substances with short half-life decay quickly → highly radioactive.
● Substances with long half-life decay slowly → less active but long-lasting.

🕒 Mean Life

● Mean life is the average lifetime of all radioactive atoms before they decay.
● It tells how long, on average, one atom of a radioactive substance exists before decaying.
● Mean life is represented by the symbol τ (tau).
● Every atom does not decay at the same time — some decay early, some late —
→ Mean life gives the average of all these decay times.
● Mean life is related to the decay constant (λ).
● A larger decay constant (λ) means the substance decays quickly → short mean life.
● A smaller decay constant means slower decay → long mean life.
● Mean life is always greater than the half-life of the same substance.
● Mean life is a fixed value for each radioactive element.
● It does not depend on external conditions like temperature, pressure, or state.

🌟 Bohr’s Atomic Model – Explanation

● Proposed by Niels Bohr in 1913 to explain the structure of the hydrogen atom.
● Electrons revolve around the nucleus in fixed circular orbits called energy levels or shells.
● These permitted orbits are stable and electrons do not radiate energy while revolving in them.
● Each orbit has a fixed energy and is denoted by
K, L, M, N… or n = 1, 2, 3, 4…
● Electrons can jump from a lower energy level to a higher level by absorbing energy.
● Electrons can fall from a higher energy level to a lower level by emitting energy in the form of light (photons).
● The energy of the emitted or absorbed photon is given by:
E = E₂ – E₁
● Angular momentum of the electron is quantized, allowed only in discrete values:
mvr = n (h/2π)
● Only certain orbits are allowed where the electron’s angular momentum fits as whole-number multiples of h/2π.
● The model explains the line spectrum of hydrogen and the formation of spectral lines.
● Bohr’s model corrected the failures of Rutherford’s model by introducing quantized orbits.

🌈 Spectral Series of Hydrogen

● When an electron in a hydrogen atom jumps between energy levels, it emits or absorbs photons of specific wavelengths.
● These wavelengths form distinct line spectra called spectral series.
● Each series corresponds to electrons falling to a specific lower energy level (n₁).
● The wavelength of each line is given by the Rydberg formula:
1/λ = R (1/n₁² − 1/n₂²)
where R = Rydberg constant.
● Different spectral series appear in different regions of the electromagnetic spectrum.

🔢 Types of Hydrogen Spectral Series
⭐ 1. Lyman Series

● Electron transition to n₁ = 1

● Lies in Ultraviolet (UV) region

● Example: n₂ = 2, 3, 4… → 1

⭐ 2. Balmer Series

● Electron transition to n₁ = 2

● Lies in Visible light region

● Only series visible to the human eye

⭐ 3. Paschen Series

● Electron transition to n₁ = 3

● Lies in Infrared (IR) region

⭐ 4. Brackett Series

● Transition to n₁ = 4

● Lies in Infrared (IR) region

⭐ 5. Pfund Series

● Transition to n₁ = 5

● Lies in Far Infrared region

⭐ 6. Humphreys Series

● Transition to n₁ = 6

● Lies in Infrared region

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