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Standard XII

Chemistry

Bohr's Model of a Hydrogen Atom

According to ...

Question

According to Bohr's theory:
$E_{n} =$ Total energy
$K_{n} =$ Kinetic energy
$V_{n} =$ Potential energy
$r^{n} =$ Radius of the nth orbit
Match List-I with List-II.

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Solution

(A) $V_{n} = - \frac{1}{4 π ϵ_{0}} (\frac{Z e^{2}}{r})$
$K_{n} = \frac{1}{8 π ϵ_{0}} (\frac{Z e^{2}}{r})$

$\Rightarrow \frac{V_{n}}{K_{n}} = - 2$
(B) $E_{n} = - \frac{Z e^{2}}{8 π ϵ_{0} r}$
$E_{n} \propto r^{- 1}$
$\Rightarrow x = - 1$
(C) Angular momentum $= \sqrt{l (l + 1)} \frac{h}{2 π} = 0$ is $1 s$ orbital. As $l$ =0 for 1s.
(D) $r_{n} = \frac{a_{0} n^{2}}{Z}$
$\Rightarrow \frac{1}{r_{n}} \propto Z$ .
So, $y = 1$

Hence, the correct answer is $A = 3; B = 2; C = 1; D = 4$

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Similar questions

Q. According to Bohr's theory,

E_{n} =

Total energy

K_{n} =

Kinetic energy

V_{n} =

Potential energy

r_{n} =

Radius of

n^{t h}

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Match the following:

Q. According to Bohr's concept,

E_{n}

is total energy,

K_{n}

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V_{n}

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r_{n}

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Q. If in Bohr's model, for unielectronic atoms, the following symbols are used,

r_{n, z} \to

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Match List-I with List-II.

Match the items in column I with their respective values in column II.
1. According to Bohr's thoery
$E_{n}$ = Total energy
$K_{n}$ = Kinetic energy
$V_{n}$ = Potential energy
$r_{n}$ = Radius of nth orbit energy

$\begin{matrix} Column I & Column II a . \frac{V_{n}}{K_{n}} = ? & p . 0 b . If radius of n^{t h} orbit \propto E_{n}^{x}, x = ? & q . - 1 c . Angular momentum in lowest orbital & r . - 2 d . \frac{1}{r_{n}} \propto Z^{y}, y = ? & s .1 \end{matrix}$

Q. If

E_{P}

and

E_{k}

represent potential energy and kinetic energy respectively, of an orbital electron, then according to Bohr's theory:

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According to Bohr's theory:En= Total energyKn= Kinetic energyVn= Potential energyrn= Radius of the nth orbitMatch List-I with List-II.

(A) Vn=−14πϵ0(Ze2r)Kn=18πϵ0(Ze2r)⇒VnKn=−2(B) En=−Ze28πϵ0rEn∝r−1⇒x=−1(C) Angular momentum =√l(l+1)h2π=0 is 1s orbital. As l=0 for 1s.(D) rn=a0n2Z⇒1rn∝Z.So, y=1Hence, the correct answer is A=3;B=2;C=1;D=4

According to Bohr's theory:
$E_{n} =$ Total energy
$K_{n} =$ Kinetic energy
$V_{n} =$ Potential energy
$r^{n} =$ Radius of the nth orbit
Match List-I with List-II.