Grade 11 : Chemistry - Atom Structure (Set 1)

Explanation: J.J. Thomson determined the charge-to-mass ratio ($e/m$) of electrons in 1897 using cathode ray discharge tube experiments, finding it to be approximately $1.76 \times 10^{11}\text{ C/kg}$.

Explanation: The number of neutrons ($N$) is given by the difference between the mass number ($A$) and the atomic number ($Z$): $$N = A - Z = 37 - 17 = 20$$

Explanation: Sodium ion $\text{Na}^+$ has $11 - 1 = 10$ electrons. Neon $\text{Ne}$ has an atomic number of 10, so it has 10 electrons. Since both have 10 electrons, they are isoelectronic.

Explanation: For a $3d$ orbital, the main shell is $n = 3$. The azimuthal quantum number $l$ corresponds to subshells as: $s=0$, $p=1$, $d=2$, $f=3$. Therefore, $l = 2$.

Explanation: The maximum number of electrons in a main energy level $n$ is given by $2n^2$. For $n = 4$, $\text{Max electrons} = 2(4)^2 = 2 \times 16 = 32$.

Explanation: The principal quantum number ($n$) determines size/energy, azimuthal ($l$) determines orbital shape, magnetic quantum number ($m_l$) determines spatial orientation, and spin ($m_s$) determines electron spin orientation.

Explanation: Energy in the $n$-th level is given by $E_n = -\frac{13.6}{n^2}\text{ eV}$. For the second excited state, $n = 3$: $$E_3 = -\frac{13.6}{3^2} = -\frac{13.6}{9} \approx -1.51\text{ eV}$$

Explanation: Using $\nu = \frac{c}{\lambda}$ with $\lambda = 600 \times 10^{-9}m$: $$\nu = \frac{3.0 \times 10^8}{600 \times 10^{-9}} = 5.0 \times 10^{14}\text{ Hz}$$

Explanation: The formula for the number of radial nodes is $n - l - 1$. For a $4p$ orbital, $n = 4$ and $l = 1$: $$\text{Radial nodes} = 4 - 1 - 1 = 2$$

Explanation: The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers ($n, l, m_l, m_s$).

Explanation: Chromium ($Z=24$) exhibits extra stability associated with a half-filled $d$-subshell ($3d^5$). An electron transfers from $4s$ to $3d$, resulting in $[\text{Ar}]\,4s^1 3d^5$.

Explanation: De Broglie proposed that matter exhibits wave properties, with wavelength inversely proportional to momentum: $\lambda = \frac{h}{p} = \frac{h}{mv}$.

Explanation: Isobars are atoms of different elements (different $Z$) with equal mass numbers ($A$). Examples include $^{40}_{18}\text{Ar}$ and $^{40}_{20}\text{Ca}$.

Explanation: The Lyman series corresponds to electron transitions to $n_1 = 1$ from higher levels ($n_2 = 2, 3, 4\dots$), producing radiation in the ultraviolet region.

Explanation: Heisenberg's Uncertainty Principle states that position and momentum cannot be measured simultaneously with absolute precision: $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$.

Explanation: Using Planck's equation $E = h\nu$: $$E = (6.626 \times 10^{-34}\text{ J}\cdot\text{s}) \times (5.0 \times 10^{14}\text{ s}^{-1}) = 3.313 \times 10^{-19}\text{ J}$$

Explanation: Orbital angular momentum is given by $L = \sqrt{l(l+1)}\frac{h}{2\pi}$. For an $s$-orbital, $l = 0$, so $L = \sqrt{0(0+1)}\frac{h}{2\pi} = 0$.

Explanation: Nitrogen ($Z=7$) has electron configuration $1s^2 2s^2 2p^3$. According to Hund's rule, the 3 electrons in the $2p$ subshell occupy separate $p_x, p_y, p_z$ orbitals with parallel spins, giving 3 unpaired electrons.

Explanation: The azimuthal quantum number $l$ can only take integer values from 0 up to $n-1$. For $n = 2$, $l$ can only be 0 or 1. Therefore $l = 2$ is impossible.

Explanation: Rutherford observed that a tiny fraction of alpha particles bounced back at large angles, proving that positive charge and mass are concentrated in a dense central region called the nucleus.