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1. Atomic Radii:

  • Remember the atomic radii trend (increases down the group). For a quick estimation, the atomic radii of Group 2 elements can be approximated as 1.5 times the ionic radii.

2. Ionic Radii:

  • The ionic radii increase down the group due to the shielding effect of the added energy levels.

3. Ionization Enthalpy:

  • Ionization enthalpy decreases down the group due to increasing atomic size and decreasing electronegativity.
  • For a rough estimate, the second ionization enthalpy is usually 2-3 times the first ionization enthalpy.

4. Melting Point:

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  • Atomic Radii:

-Increases down the group

  • Ionization Energy:
  • Decreases down the group.
  • Electronegativity:
  • Decreases down the group.
  • Melting Point:

-Increases down the group

  • Boiling Point:
  • Increases down the group.
  • Chemical Reactivity:
  • Increases down the group.

CBSE Board Exams

  • Atomic Number and Electronic Configuration:
  • Should be known.
  • Physical Properties:
  • Atomic radii, ionization energy, electronegativity, melting point, boiling point, and density.
  • Chemical Properties:
  • Oxidation states, reactivity with oxygen, hydrogen, and water; formation of halides, oxides, hydroxides, and sulfides.
  • Application:
  • Use in electronics, catalysis, and medicine.

Additional Information:

  • Group 13 elements are also known as the Boron group.

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Shortcut Methods

  • Atomic Radii:

-Increases down the group

  • Ionization Energy:
  • Decreases down the group.
  • Electronegativity:
  • Decreases down the group.
  • Melting Point:

-Increases down the group

  • Boiling Point:
  • Increases down the group.
  • Chemical Reactivity:
  • Increases down the group.

CBSE Board Exams

  • Atomic Number and Electronic Configuration:
  • Should be known.
  • Physical Properties:
  • Atomic radii, ionization energy, electronegativity, melting point, boiling point, and density.
  • Chemical Properties:
  • Oxidation states, reactivity with oxygen, hydrogen, and water; formation of halides, oxides, hydroxides, and sulfides.
  • Application:
  • Use in electronics, catalysis, and medicine.

Additional Information:

  • Group 13 elements are also known as the Boron group.

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  • Find the area of the circle with radius ‘r’.

Area = πr²

  • Find the circumference of the circle with radius ‘r’.

Circumference = 2πr

  • Find the equation of the circle with center ‘(a, b)’ and radius ‘r’.

(x - a)² + (y - b)² = r²

  • Find the equation of the tangent to the circle with center ‘(a, b)’ and radius ‘r’ at the point ‘(x1, y1)’. y - y₁ = (x - x₁) * [(y₂ - y₁)/(x₂ - x₁)]

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1. Multiplication Techniques:

  • Skip Counting: Multiply by 2, 5, 10, or 25 by repeatedly adding the number to itself.
  • Lattice Multiplication: A visual method to multiply two-digit numbers.
  • Cross Multiplication: Used for multiplying three-digit numbers.

2. Division Tricks:

  • Halving and Doubling: Repeatedly halve the divisor and double the quotient until the divisor becomes 1.
  • Factor-Digit Technique: Identify common factors in the divisor and dividend to simplify division.

3. Percentages:

  • Percentage of 100: To find a percentage of a number, first divide the number by 100 and then multiply it by the given percentage.

4. LCM (Least Common Multiple):

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NEET

  1. Finding the Area Bounded by a Curve and the x-axis:

    • Use the formula, Area = ∫[a,b] f(x) dx, where a and b are the limits of integration and f(x) is the function representing the curve.
    • Split the area into simple regions and integrate each region separately.

  2. Finding the Volume of a Solid Revolution:

    • Use the formula, Volume = ∫[a,b] πf(x)^2 dx, where a and b are the limits of integration, f(x) is the function representing the curve being revolved, and π is the constant pi (approximately 3.14).
    • Alternatively, you can use the Disk Method or Shell Method to find the volume.

  3. Evaluating Improper Integrals:

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1. A uniform rod of length L and mass M is hinged at one end and can rotate freely in a vertical plane. The rod is released from a horizontal position. What is the magnitude of the torque acting on the rod just before it reaches the vertical position?

Solution:

$$At\space position \theta, $$ $$\tau_{net}=-mgsin\theta L/2$$ $$\alpha=-\dfrac{3g}{2L}sin\theta$$

$$\omega^2=\omega_0^2-\int_{0}^{\theta}2\alpha d\theta$$

$$\omega^2=\omega_0^2+\dfrac{3g}{L}cos\theta$$

At vertical position,$$\theta=\pi/2$$

Substituting the value of ω, we get, $$\omega^2=\omega_0^2-3g$$

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1. Resonant Frequency

$$f_r = \frac{1}{2\pi\sqrt{LC}}$$

Remember:

  • Resonant frequency is inversely proportional to the square root of both inductance and capacitance.
  • Higher the values of L and C, Lower is the resonant frequency.

2. Time Constant

$$ \tau = RC$$

Remember:

  • Time constant is simply the product of resistance and capacitance.
  • Higher the resistance, higher the time constant.
  • Higher the capacitance, higher the time constant.

3. Initial Current

$$ I_{initial} = \frac{V_0}{R} $$

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