We read your photo as:

Please the answers should be in English

English

ScanSolve AI Answer

Answer

The equation is homogeneous.\text{The equation is homogeneous.}

Step-by-step solution

5 steps

To show that the equation λ=hmv\lambda = \frac{h}{mv} is homogeneous, we need to verify that the units on both sides of the equation are the same.

  1. Identify the units of the physical quantities.

    • λ\lambda is wavelength, its unit is meter (m).
    • hh is Planck's constant, its unit is Joule-second (J·s).
    • mm is mass, its unit is kilogram (kg).
    • vv is velocity, its unit is meter per second (m/s).

  2. Express the unit of Planck's constant (hh) in fundamental SI units (kg, m, s).

    The unit of energy, Joule (J), is defined as the work done by a force of 1 Newton over a distance of 1 meter.

    1 J=1 N⋅m1 \text{ J} = 1 \text{ N} \cdot \text{m}

    Force (Newton, N) is defined by Newton's second law (F=maF=ma):

    1 N=1 kg⋅m/s21 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2

    So, the unit of Joule is:

    1 J=(1 kg⋅m/s2)⋅m=1 kg⋅m2/s21 \text{ J} = (1 \text{ kg} \cdot \text{m/s}^2) \cdot \text{m} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^2

    Therefore, the unit of Planck's constant hh is:

    [h]=J⋅s=(kg⋅m2/s2)⋅s=kg⋅m2/s[h] = \text{J} \cdot \text{s} = (\text{kg} \cdot \text{m}^2/\text{s}^2) \cdot \text{s} = \text{kg} \cdot \text{m}^2/\text{s}

  3. Calculate the units of the right-hand side of the equation (hmv\frac{h}{mv}).

    The units of the numerator are:

    [h]=kg⋅m2/s[h] = \text{kg} \cdot \text{m}^2/\text{s}

    The units of the denominator are:

    [m]⋅[v]=kg⋅(m/s)[m] \cdot [v] = \text{kg} \cdot (\text{m/s})

    Now, we divide the units of the numerator by those of the denominator:

    [hmv]=kg⋅m2/skg⋅m/s\left[\frac{h}{mv}\right] = \frac{\text{kg} \cdot \text{m}^2/\text{s}}{\text{kg} \cdot \text{m/s}}

  4. Simplify the units of the right-hand side.

    [hmv]=kg⋅m2s×skg⋅m\left[\frac{h}{mv}\right] = \frac{\text{kg} \cdot \text{m}^2}{\text{s}} \times \frac{\text{s}}{\text{kg} \cdot \text{m}} [hmv]=kg⋅m2⋅ss⋅kg⋅m=m\left[\frac{h}{mv}\right] = \frac{\cancel{\text{kg}} \cdot \text{m}^{\cancel{2}} \cdot \cancel{\text{s}}}{\cancel{\text{s}} \cdot \cancel{\text{kg}} \cdot \cancel{\text{m}}} = \text{m}

  5. Compare the units of both sides.

    The units of the left-hand side of the equation ([λ][\lambda]) are meters (m).
    The units of the right-hand side of the equation ([hmv]\left[\frac{h}{mv}\right]) are also meters (m).

    Since the units on both sides of the equation are identical (meters), the equation is homogeneous.

    The equation is homogeneous.\text{The equation is homogeneous.}

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More English Questions

QPlease answer the question . The answers should be in English pleaseQPlease can you give answers in EnglishQPlease solve the questions and the answers should be in EnglishQPlease I need answers in EnglishQAnd plz the answers should be in English
See all English questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp