Emission transitions in the Paschen series end at orbit n = 3 and start from orbit n and can be represented as v = 3 .29 × 10 15 ( Hz ) 1 3 2 – 1 n 2 . Calculate the value of n if the transition is observed at 1285 nm . Find the region of the spectrum.

Given: Wavelength of transition = 1285 nm = 1285 × 10 - 9 m ν = 3 .29 × 10 15 1 3 2 - 1 n 2 Since, ν = c λ = 3 × 10 8 ms - 1 1285 × 10 - 9 m Now, ν = 2 .33 × 10 14 s - 1 3 .29 × 10 15 1 9 - 1 n 2 = 2 .33 × 10 14 1 9 - 1 n 2 = 2 .33 × 10 14 3 .29 × 10 15 1 9 - 0 .7082 × 10 - 1 = 1 n 2 ⇒ 1 n 2 = 1 .1 × 10 - 1 - 0 .7082 × 10 - 1 1 n 2 = 4 .029 × 10 - 2 n = 14.029 × 10 - 2 n = 4 .98 n = 5 Hence, for the transition to be observed at 1285 nm , n = 5 . The spectrum lies in the infra-red region.

Calculate the wavelength for the emission transition if it starts from the orbit having radius 1 .3225 nm and ends at 211 .6 pm . Name the series to which this transition belongs and the region of the spectrum.

Radius of the initial orbit = 1 . 3225 nm Radius of the final orbit = 211 . 6 pm The radius of the nth orbit of hydrogen-like particles is given by, r = 0 .529 n 2 Z Å r = 52 . 9 n 2 Z pm For radius ( r 1 ) = 1 .3225 nm = 1 .32225 × 10 - 9 m n 1 2 = r 1 Z 52 .9 = 1322 .25 × 10 - 12 m n 1 2 = 1322 .25 Z 52 .9 = 1322 .25 pm Similarly, n 2 2 = 211 .6 Z 52 .9 n 1 2 n 2 2 = 1322 .5 211 .6 n 1 2 n 2 2 = 6 .25 n 1 n 2 = 2 .5 n 1 n 2 = 25 10 = 5 2 ⇒ n 1 = 5 and n 2 = 2 Thus, the transition is from the 5 th orbit to the 2 nd orbit. It belongs to the Balmer series. Wave number ( v - ) for the transition is given by, 1 .097 × 10 7 1 2 2 - 1 5 2 m - 1 = 1 .097 × 10 7 m - 1 21 100 = 2 .303 × 10 6 m - 1 Wavelength (λ) associated with the emission transition is given by, λ = 1 / ν = 1 / 2 .303 × 10 6 m - 1 = 0 .434 × 10 - 6 m - 1 = 434 nm

The velocity associated with a proton moving in a potential difference of 1000 V is 4 .37 × 10 5 ms – 1 . If the hockey ball of mass 0 .1 kg is moving with this velocity, calculate the wavelength associated with this velocity.

Given: Potential difference = 1000 V Velocity of the proton = 4 .37 × 10 5 ms – 1 Mass of the hockey ball = 0 . 1 kg We know: Planck’s constant ( h ) = 6 .62 × 10 - 34 According to de-Broglie’s expression, λ = h mν = 6 .62 × 10 - 34 0 .1 kg 4 .37 × 10 5 ms - 1 = 1 .516 × 10 - 38 m Therefore, the wavelength associated with this velocity is 1 . 516 × 10 - 38 m .

HARD

11th CBSE

IMPORTANT

Earn 100

If the photon of the wavelength $150 pm$ strikes an atom and one of its inner bound electrons is ejected out with a velocity of $1 .5 \times 10^{7} {ms}^{- 1},$ calculate the energy with which it is bound to the nucleus.

Important Questions on Structure of Atom

HARD

11th CBSE

IMPORTANT

Textbook for Class XI Chemistry Part I>Chapter 2 - Structure of Atom>EXERCISES>Q 2.55

Emission transitions in the Paschen series end at orbit

n = 3

and start from orbit

n

and can be represented as

v = 3 .29 \times 10^{15} (Hz) [\frac{1}{3^{2}} - \frac{1}{n^{2}}]

. Calculate the value of n if the transition is observed at

1285 nm

. Find the region of the spectrum.

HARD

11th CBSE

IMPORTANT

Textbook for Class XI Chemistry Part I>Chapter 2 - Structure of Atom>EXERCISES>Q 2.56

Calculate the wavelength for the emission transition if it starts from the orbit having radius

1 .3225 nm

and ends at

= 7 .6 \times 10^{3} eV

Name the series to which this transition belongs and the region of the spectrum.

HARD

11th CBSE

IMPORTANT

Textbook for Class XI Chemistry Part I>Chapter 2 - Structure of Atom>EXERCISES>Q 2.57

Dual behavior of matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other type of material. If the velocity of the electron in this microscope is

1 .6 \times 10^{6} {ms}^{- 1},

calculate de Broglie wavelength associated with this electron.

HARD

11th CBSE

IMPORTANT

Textbook for Class XI Chemistry Part I>Chapter 2 - Structure of Atom>EXERCISES>Q 2.58

Similar to electron diffraction, neutron diffraction microscope is also used for the determination of the structure of molecules. If the wavelength used here is

800 pm

, Calculate the characteristic velocity associated with the neutron.

HARD

11th CBSE

IMPORTANT

Textbook for Class XI Chemistry Part I>Chapter 2 - Structure of Atom>EXERCISES>Q 2.59

Similar to electron diffraction, neutron diffraction microscope is also used for the determination of the structure of molecules. If the wavelength used here is 800 pm, calculate the characteristic velocity associated with the neutron.

HARD

11th CBSE

IMPORTANT

Textbook for Class XI Chemistry Part I>Chapter 2 - Structure of Atom>EXERCISES>Q 2.6

The velocity associated with a proton moving in a potential difference of

1000 V

4 .37 \times 10^{5} {ms}^{- 1}

. If the hockey ball of mass

0 .1 kg

is moving with this velocity, calculate the wavelength associated with this velocity.

HARD

11th CBSE

IMPORTANT

Textbook for Class XI Chemistry Part I>Chapter 2 - Structure of Atom>EXERCISES>Q 2.61

If the position of the electron is measured within an accuracy of

\underline{+} 0 .002 nm

, calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is

h / 4 π_{m} \times 0 .05 nm

, is there any problem in defining this value.

HARD

11th CBSE

IMPORTANT

Textbook for Class XI Chemistry Part I>Chapter 2 - Structure of Atom>EXERCISES>Q 2.62

The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. If any of these combination(s) has/have the same energy lists:

1. $n = 4, l = 2, m_{l} = - 2, m_{s} = - 1 / 2$
2. $n = 3, l = 2, m_{l} = 1, m_{s} = + 1 / 2$
3. $n = 4, l = 1, m_{l} = 0, m_{s} = + 1 / 2$
4. $n = 3, l = 2, m_{l} = - 2, m_{s} = - 1 / 2$
5. $n = 3, l = 1, m_{l} = - 1, m_{s} = + 1 / 2$
6. $n = 4, l = 1, m_{l} = 0, m_{s} = + 1 / 2$

If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 1.5×107 ms-1, calculate the energy with which it is bound to the nucleus.

Important Questions on Structure of Atom

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If the photon of the wavelength $150 pm$ strikes an atom and one of its inner bound electrons is ejected out with a velocity of $1 .5 \times 10^{7} {ms}^{- 1},$ calculate the energy with which it is bound to the nucleus.