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Give the order of the following : (a) ...

Give the order of the following :
(a) 1
(b) 1000
(c ) 499
(d) 500
(e) 501)
(f) 1 AU `(1.496 xx 10^(11) m)`
(g) 1 Å `(10(-10)m )`
(h) Speed of light `(3.00 xx 10^(8) m//s)`
(i) Gravitational constant `(6.67 xx 10^(-11) N-m^(2)//kg^(2))`
(j) Avogadro constant `(6.02 xx 10^(23) mol^(-1))`
(k) Planck's constant `(6.63 xx 10^(-34) J-s)`
(l) Charge on electron `(1.60 xx 10^(-19) C)`
(m) Radius of H - atom `(5.29 xx 10^(-11)m)`
(n) Atmospheric pressure `(1.01 xx 10^(5) Pa)`
(o) Mass of earth `(5.98 xx 10^(24)kg)`
(p) Mean radius of earth `(6.37 xx 10^(6)m)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the order of magnitude for each of the given values, we will express each number in the form \( A \times 10^N \), where \( A \) is between 0.5 and 5, and \( N \) is an integer. The order of magnitude is represented by \( N \). ### Step-by-Step Solution: 1. **1**: - Write as \( 1 \times 10^0 \). - **Order of magnitude**: \( 0 \). 2. **1000**: - Write as \( 1 \times 10^3 \). - **Order of magnitude**: \( 3 \). 3. **499**: - Write as \( 4.99 \times 10^2 \). - **Order of magnitude**: \( 2 \). 4. **500**: - Write as \( 5.00 \times 10^2 \). - **Order of magnitude**: \( 2 \). 5. **501**: - Write as \( 5.01 \times 10^2 \). - **Order of magnitude**: \( 2 \). 6. **1 AU (1.496 × 10^11 m)**: - Already in scientific notation. - **Order of magnitude**: \( 11 \). 7. **1 Å (10^{-10} m)**: - Write as \( 1.0 \times 10^{-10} \). - **Order of magnitude**: \( -10 \). 8. **Speed of light (3.00 × 10^8 m/s)**: - Already in scientific notation. - **Order of magnitude**: \( 8 \). 9. **Gravitational constant (6.67 × 10^{-11} N m²/kg²)**: - Write as \( 0.667 \times 10^{-10} \). - **Order of magnitude**: \( -10 \). 10. **Avogadro constant (6.02 × 10^{23} mol^{-1})**: - Write as \( 0.602 \times 10^{24} \). - **Order of magnitude**: \( 24 \). 11. **Planck's constant (6.63 × 10^{-34} J s)**: - Write as \( 0.663 \times 10^{-33} \). - **Order of magnitude**: \( -34 \). 12. **Charge on electron (1.60 × 10^{-19} C)**: - Write as \( 1.60 \times 10^{-19} \). - **Order of magnitude**: \( -19 \). 13. **Radius of H atom (5.29 × 10^{-11} m)**: - Write as \( 0.529 \times 10^{-10} \). - **Order of magnitude**: \( -10 \). 14. **Atmospheric pressure (1.01 × 10^{5} Pa)**: - Write as \( 1.01 \times 10^{5} \). - **Order of magnitude**: \( 5 \). 15. **Mass of Earth (5.98 × 10^{24} kg)**: - Write as \( 0.598 \times 10^{25} \). - **Order of magnitude**: \( 25 \). 16. **Mean radius of Earth (6.37 × 10^{6} m)**: - Write as \( 0.637 \times 10^{7} \). - **Order of magnitude**: \( 7 \). ### Final Orders of Magnitude: - 1: \( 0 \) - 1000: \( 3 \) - 499: \( 2 \) - 500: \( 2 \) - 501: \( 2 \) - 1 AU: \( 11 \) - 1 Å: \( -10 \) - Speed of light: \( 8 \) - Gravitational constant: \( -10 \) - Avogadro constant: \( 24 \) - Planck's constant: \( -34 \) - Charge on electron: \( -19 \) - Radius of H atom: \( -10 \) - Atmospheric pressure: \( 5 \) - Mass of Earth: \( 25 \) - Mean radius of Earth: \( 7 \)
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Knowledge Check

  • The value of universal gravitational constant G = 6.67 xx 10^(-11) N m^(2) kg^(-2) . The value of G in units of g^(-1) cm (^(3)s^(-2) is

    A
    `6.67 xx 10^(-8)`
    B
    `6.67 xx 10^(-7)`
    C
    `6.67 xx 10^(-9)`
    D
    `6.67 xx 10^(10)`
  • The energy of a photon wavelength k = 1 meter is (Planck's constant = 6.625 xx 10^(-34) Js, speed of light = 3 xx 10^(8) m//s )

    A
    `1.988 xx 10^(-23) J`
    B
    `1.988 xx 10^(-28) J`
    C
    `1.988 xx 10^(-30) J`
    D
    `1.988 xx 10^(-25) J`
  • Uncertainty in position of particle of 25 g in space is 10^(-15) m . Hence , uncertainty in velocity (ms^(-1)) is : (Planck's constant , h = 6.63 xx 10^(-34) Js)

    A
    `2.1 xx 10^(-18)`
    B
    `2.1 xx 10^(-34)`
    C
    `0.5 xx 10^(-34)`
    D
    `5.0 xx 10^(-24)`
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