Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

The mass of an electron is 9.1 × 10^–31 kg. If its K.E. is 3.0 × 10^–25 J, calculate its wavelength.

Calculate the amount of carbon dioxide that could be produced when

(i) 1 mole of carbon is burnt in air.

(ii) 1 mole of carbon is burnt in 16 g of dioxygen.

(iii) 2 moles of carbon are burnt in 16 g of dioxygen.

Calculate the wavelength of an electron moving with a velocity of 2.05 × 10⁷ ms^–1.

Balance the following redox reactions by ion – electron method :

(a) MnO₄ ^– (aq) + I ^– (aq) → MnO_{2 (s)} + I_2(s) (in basic medium)

(b) MnO₄ ^– (aq) + SO_{2 (g)} → Mn²⁺ (aq) + HSO₄^– (aq) (in acidic solution)

(c) H₂O_{2 (aq)} + Fe ²⁺ (aq) → Fe³⁺ (aq) + H₂O (l) (in acidic solution)

(d) Cr₂O₇ ^2– + SO_2(g) → Cr³⁺ _(aq) + SO₄^2– (aq) (in acidic solution)

In a process, 701 J of heat is absorbed by a system and 394 J ofwork is done by the system. What is the change in internal energy for the process?

What will be the minimum pressure required to compress 500 dm³ of air at 1 bar to 200 dm³ at 30°C?

In a reaction A + B2 → AB2 Identify the limiting reagent, if any, in the following reaction mixtures.

(i) 300 atoms of A + 200 molecules of B

(ii) 2 mol A + 3 mol B

(iii) 100 atoms of A + 100 molecules of B

(iv) 5 mol A + 2.5 mol B

(v) 2.5 mol A + 5 mol B

At 0°C, the density of a certain oxide of a gas at 2 bar is same as that of dinitrogen at 5 bar. What is the molecular mass of the oxide?

Which one of the following will have largest number of atoms?

(i) 1 g Au (s)

(ii) 1 g Na (s)

(iii) 1 g Li (s)

(iv) 1 g of Cl2(g)

Density of a gas is found to be 5.46 g/dm³ at 27 °C at 2 bar pressure. What will be its density at STP?

The equilibrium constant for a reaction is 10. What will be the value of ΔG⁰ ?  R = 8.314 JK^–1 mol^–1, T = 300 K.

Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

(a) Human muscle-fluid, 6.83

(b) Human stomach fluid, 1.2

(c) Human blood, 7.38

(d) Human saliva, 6.4.

What do you expect the nature of hydrides is, if formed by elements of atomic numbers 15, 19, 23 and 44 with dihydrogen? Compare their behaviour towards water.

Define hydrogen bond. Is it weaker or stronger than the van der Waals forces?

The electron energy in hydrogen atom is given by En = (–2.18 × 10^–18)/n² J. Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of light in cm that can be used to cause this transition?

Whenever a reaction between an oxidising agent and a reducing agent is carried out, a compound of lower oxidation state is formed if the reducing agent is in excess and a compound of higher oxidation state is formed if the oxidising agent is in excess. Justify this statement giving three illustrations.

How does the atomic hydrogen or oxy-hydrogen torch function for cutting and welding purposes? Explain.

Identify the reagents shown in bold in the following equations as nucleophiles or electrophiles:

(a) CH₃COOH  +  HO^-  →   CH₃COO^- + H₂O

(b) CH₃COCH₃  +  C^-N  →  (CH₃)₂ C (CN) (OH)

(c) C₆H₅  +  CH₃C⁺O  →  C₆H₅COCH₃

Given the standard electrode potentials,

K⁺/K = -2.93V, Ag⁺/Ag = 0.80V,

Hg²⁺/ Hg = 0.79V

Mg²⁺/ Mg = -2.37V. Cr³⁺/ Cr = -0.74V

Arrange these metals in their increasing order of reducing power.

Addition of HBr to propene yields 2-bromopropane, while in the presence of benzoyl peroxide, the same reaction yields 1-bromopropane. Explain and give mechanism.