Q: According to Bohr's theory of hydrogen-atom, for the electron in the \$n^{th}\$ permissible orbit

Angular Momentum Quantisation:\$ mvr = \cfrac{nh}{2 \pi}\$ ------------(1)Centripetal force:\$\cfrac{k(e)e}{r^2} = \cfrac{mv^2}{r}\$ ----------------(2)\$v^2 r = \cfrac{ke^2}{m}\$Substituting (1) in (2)\$ v= \cfrac{2 \pi ke^2}{n h}\$Energy: \$E = 13.6 \cfrac{Z^2}{n^2}\$ -----------(3)Linear Momentum:\$mvr = nh/2 \pi\$\$mv = \cfrac{nh}{2 \pi r}\$ ---------------(4)From the concept attached:\$r \propto n^2\$ -----------------(5)Hence, \$ mv \propto \cfrac{1}{n}\$ by (6)and \$ U = 2KE\$\$ E \propto \cfrac{1}{n^2}\$ (concept attached)

Q: If Aufbau rule is not obeyed and the electronic filling occurs orbit by orbit till saturation is reached (for a given principal quantum number \$n\$, electrons are filled in the increasing order of azimuthal quantum number \$l\$), then the percentage change in sum of all \$(n + l)\$ values for unpaired electrons in an atom of iron is \$10x\$. What is the value of \$x\$?

When \$n+l\$ rule is obeyed, the configuration is \$^{26}Fe= 1s^{2}, 2s^{2}, 2p^{6}, 3s^{2}, 3p^{6}, 4s^{2}, 3d^{6}.\$Since, \$(n+l)\$ for each unpaired electron is \$5\$, so for \$4\$ unpaired electrons in \$^{26}Fe\$, \$(n+l)\$ is \$5\times 4= 20\$.When \$n+l\$ rule is not obeyed, the configuration is \$^{26}Fe= 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 3d^{8}.\$Since, \$(n+l)\$ for each unpaired electron is \$5\$, so for \$2\$ unpaired electrons in \$^{26}Fe\$, \$(n+l)\$ is \$5\times 2= 10\$.Now,% change \$= \dfrac{20-10}{20} \times 100 = 50 = 10x\$.\$\therefore x=5.\$

Q: The energy of separation of an electron is \$30.6\ eV\$ moving in an orbit of \$Li^{2+}\$. The number of waves made by the electron in one complete revolution in the orbit is:

As the energy of separation of an electron is \$30.6 eV\$ means it has this much energy in the ground state.By calculation, as \$E = -\displaystyle \dfrac {13.6Z^{2}}{n^{2}}\$;Here \$Z\$ is \$3\$, \$n=2\$So, the number of waves made by the electron in one complete revolution in the orbit is \$2\$.

Q: What principle is violated here?

Laws of Motion:Newtons second law: \$F = ma\$Without any force, the atom cannot accelerate.Conservation of Momentum:The linear momentum of the atom can't change without any external force acting on it.

Q: Maximum number of electrons in a subshell of an atom is determined by the following:

Hint Quantum number: It is defined as the set of numbers which describes the position and energy of electrons in an atom. There are four quantum numbers: principal, azimuthal, magnetic and spin quantum numbers. Explanation Step 1: Determine the maximum number of subshells The principle quantum number (\$n\$) describe the distance between the nucleus and the electrons.The azimuthal quantum number (\$l\$) is given by (\$n - l\$) We know that the maximum number of subshells is equal to is \$\left( 2l+1 \right)\$. Step 2: Determine the maximum number of electrons in a subshellMaximum electrons a subshell can accommodate is \$2\$ Therefore, the total number of electrons in a subshell is \$2\left( 2l+1 \right)=\left( 4l+2 \right)\$ Thus, maximum number of electrons in a subshell is \$( 4l+2)\$ Final answer The correct answer is option (D).

Q: Choose the correct observation.

\$\mathrm{H}\mathrm{e}\$ and \$\mathrm{L}\mathrm{i}^{+}\$ have 2 electrons. Isoelectronic species have same spectra.According to Pauli's exclusion pinciple, two electrons in a shell should have opposite spins.Only orbitals aligning along the axis participate favourably in the hybridization because they have the same symmetry. Hence, \$\mathrm{d}_{z^{2}}\$ orbitals participate in \$\mathrm{s}\mathrm{p}^{3}\mathrm{d}\$ hybridization.

Q: For the hydrogen atom, the energy of the electron is defined by the factor \$E_n=-13.58/n^2 eV\$. Here n is positive integer. The minimum quantity of energy which it can absorb in its primitive stage is:

\$E_n=\dfrac {-13.58}{n^2}\$In primitive stage at \$n=1, E_1=-13.58 eV\$Minimum energy in excited stage,\$n=2,\quad E_2=-3.395 eV\$Energy absorbed \$=-3.395+13.58=10.19eV\$Hence, the correct option is D

Question 1

According to Bohr's theory of hydrogen-atom, for the electron in the $n^{th}$ permissible orbit

Accepted Answer

Angular Momentum Quantisation:$ mvr = \cfrac{nh}{2 \pi}$                    ------------(1)Centripetal force:$\cfrac{k(e)e}{r^2} = \cfrac{mv^2}{r}$               ----------------(2)$v^2 r = \cfrac{ke^2}{m}$Substituting (1) in (2)$ v= \cfrac{2 \pi ke^2}{n h}$Energy: $E = 13.6 \cfrac{Z^2}{n^2}$          -----------(3)Linear Momentum:$mvr = nh/2 \pi$$mv = \cfrac{nh}{2 \pi r}$ ---------------(4)From the concept attached:$r \propto n^2$   -----------------(5)Hence, $ mv \propto \cfrac{1}{n}$ by (6)and $ U = 2KE$$ E \propto \cfrac{1}{n^2}$  (concept attached)

Question 2

If Aufbau rule is not obeyed and the electronic filling occurs orbit by orbit till saturation is reached (for a given principal quantum number $n$ , electrons are filled in the increasing order of azimuthal quantum number $l$ ), then the percentage change in sum of all $(n + l)$ values for unpaired electrons in an atom of iron is $10 x$ . What is the value of $x$ ?

Accepted Answer

When $n+l$ rule is obeyed, the configuration is $^{26}Fe= 1s^{2}, 2s^{2}, 2p^{6}, 3s^{2}, 3p^{6}, 4s^{2}, 3d^{6}.$Since, $(n+l)$ for each unpaired electron is $5$, so for $4$ unpaired electrons in $^{26}Fe$, $(n+l)$ is $5\times 4= 20$.When $n+l$ rule is not obeyed, the configuration is $^{26}Fe= 1s^{2}   2s^{2}   2p^{6}   3s^{2}   3p^{6}   3d^{8}.$Since, $(n+l)$ for each unpaired electron is $5$, so for $2$ unpaired electrons in $^{26}Fe$, $(n+l)$ is $5\times 2= 10$.Now,% change $= \dfrac{20-10}{20} \times 100 = 50 = 10x$.$\therefore x=5.$

Question 3

The energy of separation of an electron is $30.6\ eV$ moving in an orbit of $Li^{2+}$. The number of waves made by the electron in one complete revolution in the orbit is:

Accepted Answer

As the energy of separation of an electron is $30.6 eV$ means it has this much energy in the ground state.By calculation, as $E = -\displaystyle \dfrac {13.6Z^{2}}{n^{2}}$;Here $Z$ is $3$, $n=2$So, the number of waves made by the electron in one complete revolution in the orbit is $2$.

Question 4

If the principle quantum number n = 6, the correct sequence of filling of electron will be :

Accepted Answer

If the principle quantum number n = 6, the correct sequence of filling of electron will be: $ns\rightarrow(n - 2)f\rightarrow(n - 1)d\rightarrow$np.Here, $n=6$. Hence, the correct sequence of filling of electron will be $6s\rightarrow4f\rightarrow5d\rightarrow$$6p$.Hence, option D is correct.

Question 5

The orbital diagram in which aufbau principle is violated is:

Accepted Answer

Hint: Aufbau principle states that electrons getting filled in the orbitals in the increasing order of energy.Step 1: The energy of an orbital is directly proportional to the $(n + l)$ value.The $(n + l)$ value for $2s$  level:For $2s$ energy level-$n = 2$ Where $n$ is the principal quantum number and $l$ is the azimuthal quantum number.For $s$ orbital, $l=0$So, $(n + l) = 2 + 0$ $(n + l) = 2$ Step 2:The $(n + l)$ value for $2p$ level:For $2p$ energy level-$n = 2$ Where $n$ is the principal quantum number and $l$ is the azimuthal quantum number.For $p$ orbital, $l=1$So, $(n + l) = 2 + 1$ $(n + l) = 3$ Step 3:Comparison of $(n + l)$ value of two energy levels:As the value of $(n + l)$ for $2s$ orbital is less than that of $2p$ orbital so $2s$ orbital has lower energy than $2p$ orbital. Therefore $2s$ orbital will get filled first then $2p$ orbital will starts filling.Final answer:So the orbital diagram in which Aufbau principle is violated is option (B).So the correct option is (B).

Question 6

What principle is violated here?

Accepted Answer

Laws of Motion:Newtons second law: $F = ma$Without any force, the atom cannot accelerate.Conservation of Momentum:The linear momentum of the atom can't change without any external force acting on it.

Question 7

In Bohr's model of an atom :

Accepted Answer

According to Bohr's model of an atom,(i) Electrons revolve around the nucleus in circular orbits.(ii) These circular orbits are also called as stationary orbits or shells because as long as an electron is in this particular orbit, it neither gains nor loses energy.(iii) Every stationary shell is associated with a definite amount of energy.(iv) The energy of orbits increases as we move away from the nucleus.Hence, options (A), (B) and (C) are correct.

Question 8

Maximum number of electrons in a subshell of an atom is determined by the following:

Accepted Answer

Hint &#10;&#10;Quantum number: It is defined as the set of numbers which describes the position and energy of electrons in an atom. There are four quantum numbers: principal, azimuthal, magnetic and spin quantum numbers.&#10;&#10;Explanation &#10;&#10;Step 1: Determine&#10;the maximum number of subshells&#10;&#10;The principle quantum number ($n$) describe the distance between the nucleus and the electrons.The azimuthal quantum number ($l$) is given by ($n - l$)&#10;&#10;We know that the maximum number of subshells is equal to is $\left( 2l+1 \right)$.&#10;&#10;Step 2: Determine the maximum number of electrons in a subshellMaximum electrons a subshell can accommodate is $2$&#10;&#10;Therefore, the total&#10;number of electrons in a subshell is &#10;&#10;$2\left( 2l+1&#10;\right)=\left( 4l+2 \right)$&#10;&#10;Thus, maximum&#10;number of electrons in a subshell is $( 4l+2)$&#10;&#10;Final answer&#10;&#10;The correct answer&#10;is option (D).

Question 9

Choose the correct observation.

Accepted Answer

$\mathrm{H}\mathrm{e}$ and $\mathrm{L}\mathrm{i}^{+}$ have 2 electrons. Isoelectronic species have same spectra.According to Pauli's exclusion pinciple, two electrons in a shell should have opposite spins.Only orbitals aligning along the axis participate favourably in the hybridization because they have the same symmetry. Hence, $\mathrm{d}_{z^{2}}$ orbitals participate in $\mathrm{s}\mathrm{p}^{3}\mathrm{d}$ hybridization.

Question 10

For the hydrogen atom, the energy of the electron is defined by the factor $E_n=-13.58/n^2 eV$. Here n is positive integer. The minimum quantity of energy which it can absorb in its primitive stage is:

Accepted Answer

$E_n=\dfrac {-13.58}{n^2}$In primitive stage at $n=1, E_1=-13.58 eV$Minimum energy in excited stage,$n=2,\quad E_2=-3.395 eV$Energy absorbed $=-3.395+13.58=10.19eV$Hence, the correct option is D

Structure Of Atom

Chemistry
8422 Views

According to Bohr's theory of hydrogen-atom, for the electron in the $n^{t h}$ permissible orbit

The energy of separation of an electron is $30.6 e V$ moving in an orbit of $L i^{2 +}$ . The number of waves made by the electron in one complete revolution in the orbit is:

If the principle quantum number n = 6, the correct sequence of filling of electron will be :

The orbital diagram in which aufbau principle is violated is:

What principle is violated here?

In Bohr's model of an atom :

Maximum number of electrons in a subshell of an atom is determined by the following:

Choose the correct observation.

For the hydrogen atom, the energy of the electron is defined by the factor $E_{n} = - 13.58 / n^{2} e V$ . Here n is positive integer. The minimum quantity of energy which it can absorb in its primitive stage is:

Structure Of Atom

Chemistry 8422 Views

According to Bohr's theory of hydrogen-atom, for the electron in the nth permissible orbit

The energy of separation of an electron is 30.6 eV moving in an orbit of Li2+. The number of waves made by the electron in one complete revolution in the orbit is:

If the principle quantum number n = 6, the correct sequence of filling of electron will be :

The orbital diagram in which aufbau principle is violated is:

What principle is violated here?

In Bohr's model of an atom :

Maximum number of electrons in a subshell of an atom is determined by the following:

Choose the correct observation.

For the hydrogen atom, the energy of the electron is defined by the factor En​=−13.58/n2eV. Here n is positive integer. The minimum quantity of energy which it can absorb in its primitive stage is:

Chemistry
8422 Views

According to Bohr's theory of hydrogen-atom, for the electron in the $n^{t h}$ permissible orbit

The energy of separation of an electron is $30.6 e V$ moving in an orbit of $L i^{2 +}$ . The number of waves made by the electron in one complete revolution in the orbit is:

For the hydrogen atom, the energy of the electron is defined by the factor $E_{n} = - 13.58 / n^{2} e V$ . Here n is positive integer. The minimum quantity of energy which it can absorb in its primitive stage is: