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Class 12th Solutions

What is the apparent molecular mass (in gm/mol) of a weak acid, HA (molar mass = 30.0 gm/mol) in an aqueous solution, which shows elevation in boiling point by $0.0156 ° C ?$

[Given: pK_a (HA) = 2.0, K_b (H₂O) = 0.52 K kg mol^-1]

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Vishal Baghel

Contributor-Level 10

$i = \frac{m_{t h e o r}}{m_{a p p}} = \frac{30}{m_{a p p}}$

$Δ T_{b} = i k_{b} . m] {H A}_{m - x}^{m} = {H^{+}}_{x}^{-} + {A^{-}}_{x}^{-}$

$0.0156 = (\frac{m * x}{m}) * 0.52 * m$

m + x = 0.03

$\Rightarrow x = 0.01 \to i = 1.5 = \frac{30}{m_{a p p}} \Rightarrow m_{a p p p} = 20$

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Class 12th Chemistry

Hydrogenation of the above compound in the presence of poisoned palladium catalyst gives

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Vishal Baghel

Contributor-Level 10

Addition on triple bond takes place by the addition of hydrogen

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Class 12th Physics Moving Charges and Magnetism

In gravity free space, a bead of charge $1 μ C$ and mass 3mg is threaded on a rough rod of friction coefficient $μ$ = 0.3. A magnetic field of magnitude 0.2 T exists perpendicular to the rod. The bead is projected along the rod with a speed 4m/s. How much distance (in m) will the bead cover before coming to rest?

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Vishal Baghel

Contributor-Level 10

N = qvB

$- μ q v B = \frac{m d v}{d t} = m v \frac{d v}{d S}$

$μ q B S = m v$

$S = \frac{3 * 1 0^{- 6} * 4}{0.3 * 1 0^{- 6} * 0.2} = 200 m$

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Class 12th Physics Ray Optics and Optical Instruments

You are given a converging lens with equal radii of curvature and a diverging lens with the same radii of curvature as those of the converging lens. The lenses are made of material with n = 1.50, the radii of curvature are all 35cm. They are placed at opposite ends of a tube 15cm long, and the nearer lens which is converging is 10cm from an object. What is the location of the image that results from the two refractions? Write the final distance (in cm) from diverging lens.

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Vishal Baghel

Contributor-Level 10

$\frac{1}{u} + \frac{1}{- 10} = \frac{1}{35}$

$\begin{array}{l} \frac{1}{u} = \frac{1}{35} - \frac{1}{10} = \frac{2 - 7}{70} = \frac{- 1}{14} \\ \frac{1}{u} = \frac{- 1}{35} - \frac{1}{29} = \frac{- 64}{35 * 29} \\ u = \frac{35 * 29}{64} = 15.85 t o 15.86 \end{array}$

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Class 12th Physics

An electron moves in the field produced by a charged sphere of radius 10cm along the radius connecting the points separated by 12 and 15 cm from the centre of the sphere. The velocity of the electron changes thereby from 2 * 10⁵ to 2 * 10⁶ m/s. Determine the surface charge (in nC/m²) density of the sphere. (Mass of electron = 9.1 * 10^-31kg)

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Vishal Baghel

Contributor-Level 10

$\frac{k Q e}{0.12} + \frac{1}{2} m u^{2} = \frac{k Q e}{0.15} + \frac{1}{2} m u^{2}$

$\frac{k Q e * 0.03}{0.12 * 0.15} = \frac{1}{2} m * (v^{2} - u^{2})$

$Q = \frac{9.1 * 99 * 1 0^{- 11}}{12}$

$= \frac{75.075 * 1 0^{- 12}}{4 π * {(0.1)}^{2}} = 5.97 n C / m^{2}$

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Class 12th Physics Ray Optics and Optical Instruments

You are trying to construct a compound microscope given two lenses with focal lengths f₁ = 1.0cm and f₂ = 4.0cm. How far apart (in cm) should you place the lenses in order to obtain an angular magnification of 60? (Assume normal adjustment of microscope)

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Vishal Baghel

Contributor-Level 10

For better resolution, smaller focal length should be objective.

h0 = 1 cm fe = 4cm.

$\begin{array}{l} Q_{0} = \frac{h_{0}}{25} \\ Q = \frac{60 h_{0}}{25} = \frac{h_{I}}{4} \end{array}$

$\frac{L - 5}{1} = \frac{h_{I}}{h_{0}} = \frac{240}{25}$

L = 14.6 cm

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Class 12th Physics Wave Optics

When light of wavelength 540 nm passes through a single slit of unknown width, the diffraction pattern displays a second maximum where the first minimum of light of an unknown wavelength had been observed to fall. What is the unknown wavelength?

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Vishal Baghel

Contributor-Level 10

$\frac{λ_{1}}{w} = \frac{3 * 540}{2 w}$

$λ_{1} = 810 n m$

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Class 12th Physics

Drawing power form a 12V car battery, a 9V stabilized DC voltage is required to power a car stereo system, attached to the terminals A and B, as shown in the figure. If a Zener diode with ratings, V_z = 9V and P_max = 0.27 W, is connected as shown in the figure, for the above purpose, the minimum series resistance R_s must be:-

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Vishal Baghel

Contributor-Level 10

$i_{m a x} = \frac{P_{m a x}}{V_{z}} = \frac{3}{100}$

$∴ R_{s_{m i n}} = \frac{V_{R_{S}}}{i_{m a x}}$

$= \frac{3}{3 / 100} = 100 Ω$

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Class 12th Physics

Mass of Bromine, Selenium and Krypton are given as:-

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Vishal Baghel

Contributor-Level 10

$Q_{(i)} = (M_{B r} - M_{K r}) c^{2} > 0$

$\begin{array}{l} Q_{(i i)} = (M_{B r} - M_{S e} - 2 M_{e}) c^{2} > 0 \\ Q_{(i i)} = (M_{B r} - M_{s e}) c^{2} > 0 \end{array}$

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Class 12th Dual Nature of Radiation and Matter

The sketch shown below illustrates the apparatus and results for a famous experiment. The graph on the right is a polar plot of the number of electrons received in the detector. From the result, the experimenters were able to conclude that:-

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Vishal Baghel

Contributor-Level 10

This experiment is the famous Davission-Germer experiment which establishes wave nature of electrons.

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